[Note: This is a work in progress]
What are the odds that extraterrestrial (ET) life exists in the universe?
Carl Sagan once stated, "You put those together, lots of places, lots of organic matter, lots of time, and it seems very hard to believe that our paltry little planet is the only one that’s inhabited." 
The search for extraterrestrial intelligence (SETI) has been around since the beginning of the 20th Century, even Nikola Tesla suggesting that his wireless electrical transmission system could be used to contact beings on Mars. Here are three notable examples of SETI; (1) NASA has funded SETI studies, (2) Carl Sagan was involved in SETI research being one of the founders of the U.S. Planetary Society, partly as a vehicle for SETI studies, and (3) Stephen Hawking and Russian billionaire Yuri Milner announced a well-funded effort called Breakthrough Listen, a project to search for intelligent extraterrestrial communications in the universe. There is much effort to find ET and these are just three examples of a much longer list. The point is that millions, if not billions of dollars have been spent on SETI projects. So what are the odds that spending that kind of money will bring results? What would you think Las Vegas would give on the odds on finding ET?
First, let's define what we are talking about:
Wikipedia defines extraterrestrial life as referring "to life occurring outside of Earth which did not originate on Earth."
Merriam-Webster defines extraterrestrial as "originating, existing, or occurring outside the earth or its atmosphere."
"The Fermi paradox  is a conflict between the argument that scale and probability seem to favor intelligent life being common in the universe, and the total lack of evidence of intelligent life having ever arisen anywhere other than on the Earth." Wikipedia
"The Great Filter, in the context of the Fermi paradox, is whatever prevents non-living matter from undergoing abiogenesis, in time, to expanding lasting life as measured by the Kardashev scale." Wikipedia
What About ET Finding Us?
One article explains how long it would take to get to the nearest star system based upon the rate of using 'ionic propulsion' which current technology has "managed to reach a velocity of 56,000 km/hr (35,000 miles/hr)" it would "take over 81,000 years to traverse the 4.24 light years between Earth and Proxima Centauri."  So, if there is extraterrestrial life out there, since the age of the universe is usually accepted to be 13.8 billions years old and the earth is estimated by most authorities to be 4.8 billions years old, there is enough time for an 'advanced' life to travel to earth by now, since humans have invented a means of space travel in the relatively short time humans have existed, surely some other extraterrestrial advanced civilization has also invented a way to travel in space, yet there is no scientific evidence indicating that ET exists.
The Drake Equation and Abiogenesis
The debate about answering the question, 'what are the odds of extraterrestrial life in the universe' centers on what would be the data determining the math used for the calculation? For example, one of the more popular of such equations on this discussion is the Drake Equation, proposed by the astronomer and astrophysicist, Frank Drake, which Wikipedia says, "is a probabilistic argument used to estimate the number of active, communicative extraterrestrial civilizations in the Milky Way galaxy." What is the problem? The issue is described as, "Criticism related to the Drake equation focuses not on the equation itself, but on the fact that the estimated values for several of its factors are highly conjectural, the combined effect being that the uncertainty associated with any derived value is so large that the equation cannot be used to draw firm conclusions." Another succinct criticism of the Drake Equation are that the "uncertainties revolve around our understanding of the evolution of life, intelligence, and civilization, not physics."
One of the most problematic is the assumption that all life in the universe evolves from abiogenesis and that this happened on earth and would happen elsewhere in the universe. An article published in Scientific American by Sarah Lewin, states, "We don't know the mechanism whereby nonlife turns into life, so we have no way of estimating the odds … It may be one in a trillion trillion (it's easy to imagine that), in which case, Earth life may be unique in the observable universe," Davies told Space.com in an email. "But Pa may be quite large. We simply can't say." New Equation Tallies Odds of Life Beginning
Astrobiological Copernican Limit
"Now a group of scientists at the University of Nottingham think they’ve come up with a new “cosmic evolution”-based calculation that says that there are likely to be at least 36 ongoing intelligent civilizations in our Milky Way galaxy....[published] in The Astrophysical Journal, the new paper examines the likely number of Communicating Extra-Terrestrial Intelligent (CETI) civilizations in the Milky Way...It assumes that intelligent life comes to occur on other planets much as it has done on our own planet...The calculation—which says that there could be 36 active communicating intelligent civilizations in our home galaxy—is called the “Astrobiological Copernican Limit” by the researchers." 
The authors of the paper, Tom Westby & Christopher J. Conselice, state, "[W]e make a key assumption: since the time required for the development of communicative intelligent civilization on our own planet is of order 5 Gyr, then we propose that life will have a reasonable probability of forming on another planet such as the Earth in the habitable zone of a suitable star within our Galaxy in a similar amount of time."  They name this assumption the "Astrobiological Copernican Weak and Strong conditions."
Ethan Siegel, Forbes, points out, "Is this a good assumption? In a scientific sense, absolutely not...They not only assumed "a reasonable probability" that intelligent life will arise after about 5 billion years on an Earth-like world, but they then imposed a further assumption — what they call the Astrobiological Copernican Strong Condition — that intelligent life must form between 4.5 billion and 5.5 billion years after an Earth-like planet forms in an Earth-like orbit around a Sun-like star....If we're willing [to] make assumptions about how likely it is that life arises on planets with certain similarities to a young Earth, we can indeed draw conclusions about the likelihood of intelligent life throughout the galaxy. The only problems are that our conclusions are only as good as our assumptions, which we have no reason to believe are very good..." 
So far, mankind has been calling ET and no one is answering. What are the math odds that ET would phone us? The odds are just the same.
 Scroll down to video blank on blank, Carl Sagan on Extraterrestrials
 "Fermi was questioning the feasibility of travel between stars, but since then his query has come to represent doubts about the very existence of extraterrestrials. The astrophysicist Michael Hart explored the question formally when he argued in a 1975 paper that there had been plenty of time for intelligent life to colonize the Milky Way in the 13.6 billion years since the galaxy formed, yet we'd heard nothing from them. Hart concluded that there must be no other advanced civilizations in our galaxy." Alien civilizations may have explored the galaxy and visited Earth already, a new study says. We just haven’t seen them recently., Morgan McFall-Johnsen, Sep. 8, 2019, Business Insider
NASA Is About to Launch the Fastest Spacecraft in History. Target: The Sun!, by Meghan Bartels, Space.com
 There Are At Least 36 Intelligent Alien Civilizations In Our Galaxy, Say Scientists, Jamie Carter, Forbes
 The Astrobiological Copernican Weak and Strong Limits for Intelligent Life, Tom Westby & Christopher J. Conselice, University of Nottingham, School of Physics and Astronomy
 36 Alien Civilizations In The Milky Way? The Science Behind A Ridiculous Headline, Ethan Siegel, Forbes