If it's worth saying, but not worth its own post (even in Discussion), then it goes here.
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This is related to the Sleeping Beauty Problem, and in general the answer depends what you're trying to do with "probability". For lots and lots more, Bostrom's PhD thesis is very detailed: Anthropic Bias: Observation Selection Effects in Science and Philosophy.
Bostrom's Observation Selection Effects and Human Extinction Risks paper is less philosophical and sounds like it's more relvant to the paper you're working on.