No argument from authority. I just want principle so I can be precise.
The principle seems to be that once the event has already happened, it's safe to say that it already happened. Marvelling at how amazing it is that it happened, especially based on highly questionable calculations, puts one in great danger of invoking the Texas sharpshooter fallacy even at the best of times. Just think about how low the chances were that that bullet hit that exact spot!
Douglas Adams. He of Puddle-Hole Thinking notoriety. His argument implies a probability of 1:1 but where does he argue that? And thinking puddles - the ultimate in anthropomorphics!
No. The argument itself has little to do with probability directly and so does not actually properly imply a probability of 1:1, especially not beforehand. Probability can be applied to it, yes, but such misses the more specific focus. There are a couple quite valid and relevant points that can be taken from it, but not that. Similarly, the thinking puddles point is only really worth an eyeroll and can be simply dismissed out of hand (generally along with the one using it) if it's being used to try to undermine the validity of the actual points that the argument addresses.
If you want an example of simple and easy valid use of the analogy, it's validly used to point out that for us to be alive, our universe didn't necessarily have to be fine-tuned for our existence, but rather, that we could easily be the thing that's been "fine-tuned" (not necessarily by an actual intelligence or designer) to live in our universe. Of more importance to you, likely, the possibility of an intelligent designer is unfalsifiable, regardless, though, and the puddle analogy wasn't designed to claim otherwise. It was, however, designed to highlight a couple of the biggest conceptual flaws in arguments like the one that you seem to be trying to push. As Wudang already quoted from your later link -
We could not possibly have existed in conditions that are incompatible with the existence of observers.
This point alone is sufficient to make the entire prior probability argument (in pretty much all its forms) moot and inconclusive. A side note to that is that if we did exist in conditions that were incompatible with the existence of observers, that would be evidence of outside interference.
Ahhh, the butterfly effect. I'd agree with this. That said, the game never stops. Play enough poker games a Royal Flush is dealt at some time. Personally, I don't believe life is rare in the universe. Clearly, this seems to be the only planet at this speck of geological time that seems to have life. But even our vast solar system is but a microscopic point in the universe. There is a vast amount of matter and energy in the universe constantly reacting to their conditions.
...Intelligent life, at least, for our solar system. There's a pretty decent chance that Europa's got life, though, apparently.