There are three problems for calculating the odds: Firstly, it’s fairly clear that the organizing principle of evolution would work whenever anything in the universe becomes capable of “self-replication-with-occasional-errors”. Assuming that you need water, certain temperatures, a large moon, Jupiter, etc, etc is being *way* overly-cautious. However, we don’t yet understand the mechanism(s) by which self-replication comes about — and that’s a large enough problem to make it impossible for us to say whether life is everywhere — or whether we’re deeply, profoundly alone.
The second problem is the stipulation of intelligence. I don’t think that’s important in this discussion — would the god-fearing rule out a god if (s)he only created things as smart as lizards and birds? How about only worms and insects? I don’t get that the probability of intelligence bears on this argument. But if it did matter — it’s the other difficult part of the equation because we have no clue the probability of our level of intelligence evolving out of basic self-replicating systems. The question boils down to whether the environment favors highly complex organisms with intelligence — or whether it favors simple unicellular life and penalizes higher forms. This is an unknown on a par with the abiogenesis unknown.
The third problem is that we don’t know how big the universe is. If it’s infinite (which it might easily be) — then it doesn’t matter how astoundingly unlikely any intelligence-producing event is — so long as it’s not zero (which it isn’t, because we’re here) — then there are an infinite number of intelligent races out there. If it’s finite — then the question is tough because the actual size of the universe matters…a LOT! The limitations of the speed of light mean that we can only see just so far out there — so this is another huge unknown.
So the answer to this question is one totally unknown abiogenesis factor, multiplied by another totally unknown evolution-of-intelligence factor, multiplied by a number for the size of the universe that’s either infinite or finite-but-unknown, multiplied by a whole bunch of fairly well-known estimates…which means that the only possible answer here is “We Don’t Know”.
What we do know is that the abiogenesis factor and the intelligence-forming factor are not zero. Since any non-zero number, however small, times infinity is infinity, it follows that if the universe is infinite, then there is infinite life out there somewhere — for 100% sure and we don’t need to know any of the other numbers. If the universe is finite — then “We Don’t Know” is the only answer.
If we do find life (even super-primitive life) out there — or if we definitively pin down how abiogenesis came about — then we’ll have a rough idea what the abiogenesis factor is. Figuring out the intelligence-evolving factor is very tough — unless we get some kind of a message from another intelligent species or can detect chemicals that are definitively industrial by-products in the atmosphere of some exo-planet. It’s quite possible that further research into the big bang will tell us whether the universe is finite or infinite.
The odds are very good that we could figure out one of those three things very soon — and then we’ll know that the first two factors are big numbers — or that they don’t matter because they are non-zero and multiplied by infinity.
The problem is that absence of evidence isn’t evidence of absence — so FAILING to detect life or intelligent life doesn’t prove anything.
It’s a very large step from “absence of evidence” to “proof of God”…and that’s the real point here.