I searched this thread and was surprised nobody's mentioned the
Drake Equation. The universe is so big, and so old, it's virtually certain that there are other forms of sentient life. But time is so vast, and the speed of light so slow, that it's almost equally certain that we'll never meet any of them.
The Drake equation is good to know about, really an essential and constructive part of the discussion, I agree, but I am doubtful as to its value as a modern analytical too. I read up on the Drake equation some time ago. It’s kind of old school (1961), with certain very limiting assumptions about how intelligent life might arise—assuming it must be quite similar to what happened on earth. Kind of a stretch of an assumption when we have a sample n=1, IMHO. Also, IIRC, the variables in the Drake equation were so uncertain that even under its very limiting assumptions it facilitated a huge range of plausible outcomes. I also think I remember that it was intended as a ballpark estimator to make a broad point, and not as a serious predictive tool. YMMV, etc.
Still, the general point, that there may well be, or perhaps there is even a strong probability of, intelligent life elsewhere, but we may never cross paths because of the vastness of the Universe, I think that’s still a strong possibility to think about seriously.
But you know, the chance that lightning is going to hit you seems pretty low, until, well, it hits you, and then how did that math work out.