[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
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
 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