sigmoid

It can be seen from the plot has attained a maximum of +1 and a minimum of 0 and even though we are increasing the X value there is no significant change in the value of the function.

For higher positive value of x the function seems to be approaching plus one and for a higher negative value of x the function seems to be approaching zero.

That means the value of this function always lies between 0 and 1.

Which makes this a good candidate for a probability function.

If you look at the derivative of the sigmoid. Most part it has value zero and it becomes only active in the region where sigmoid is undergoing a transition from 0 to +1 .