the fact of the survival provide zero evidence about nuclear war extinction probability
There are a thousand 1940s universes. In 500 of them, the probability of surviving the cold war is 1⁄500 (dangerous); in the other 500, the probability of surviving is 499⁄500 (safe).
In 2018, there are 500 universes where humans survive, 1 from the dangerous class, and 499 from the safe class.
This is true, but it answers different question: not “given X, what probability that I will exist?” - which have sense only in the finite universes, but “Which of two classes of observers I most likely belong?”
There are a thousand 1940s universes. In 500 of them, the probability of surviving the cold war is 1⁄500 (dangerous); in the other 500, the probability of surviving is 499⁄500 (safe).
In 2018, there are 500 universes where humans survive, 1 from the dangerous class, and 499 from the safe class.
Updating on safeness seems eminently reasonable.
This is true, but it answers different question: not “given X, what probability that I will exist?” - which have sense only in the finite universes, but “Which of two classes of observers I most likely belong?”