Both assumptions require one to assign non-zero probabilities to metaphysically impossible hypotheses about where I am located in spacetime, such as the hypothesis that I was born in the 19th century, the hypothesis that I am a non-human or the hypothesis that it is now a Wednesday. It is usual in the discussion of these hypotheses not to worry much about such issues of metaphysical impossibility. The thought is that we are doing epistemology, not metaphysics.
Moreover, it seems reasonable to assign a credence 1/10 to the proposition that the hundredth digit of π is 3 when one hasn’t calculated that digit, even though one knows that the proposition is either necessarily true or necessarily false.
Perhaps my Aristotelian meta-epistemology can help, though. What if the right way to assign credences is not some abstract “rational” way to do so, but rather the human way—the way that our human nature calls us on us to? Our human nature specifies how we should function within a certain broad range of conditions. But outside of that range, human nature may not specify how we should function. Our nature specifies normal human locomation in earth gravity, but specifies nothing about what normal human locomation out in space should be like. Likewise, our nature specifies normal human credential behavior in many circumstances, but need not specify human credential behavior in outlandish cases like Doomsday.
Of course this raises the very hard question of which cases are within the range of cases where our nature specifies credential behavior and which are not.