Nobody can tell you without pulling numbers out of thin air. That's the point. The only thing that can be said is that the probability of intelligent life arising is greater than 0, which follows from our own existence. Beyond that, any claims about the likelihood of intelligent life are just 20th and 21st century versions of "there must be a God because the universe couldn't have arisen by chance."
Strictly speaking our own existence doesn't even tell us the probability is greater than zero. For an event to have probability zero doesn't imply it can't occur. If a number is chosen from a uniform distribution on the reals between zero and one, whatever the result is the probability of that exact result occurring was zero.
> The distinction in meaningless. We exist, ergo intelligent life can develop in this universe.
I didn't say anything contrary to this. I was just pointing out an interesting detail about probability theory.
It's impolite to edit your comment in such a way as to turn its existing replies into non-sequiturs. For the record, this comment initially cast doubt on the claim about zero probability events, hence the reply saying it was correct.
It is correct, if you split 100% across infinitely many possible outcomes, each outcome will have probability zero, still one of the possible outcomes will occur.
Yes, it requires uncountability. It could be that physics is ultimately best modelled with countable sets, but that hasn't been established and our current best physical theories are certainly full of uncountability.
The distinction between "surely" and "almost surely" [1] is "just" a curiosity about probability theory though, albeit a rather fundamental one, and I only brought it up as such. It's interesting to think about, and if you do so it quickly brings you up against deep philosophical questions about what probability means.