Thanks... whatever the correct resolution is, violating Bayes's Theorem seems a bit drastic!

My suspicion is that A contains indexical evidence (summarized as something like "I have just woken up as Beauty, and remember going to sleep on Sunday and the story about the coin-toss"). The indexical term likely means that P[A] is not equal to 1 though exactly what it is equal to is an interesting question.

I don't personally have a worked-out theory about indexical probabilities, though my latest WAG is a combination of SIA and SSA, with the caveat I mentioned on infinite cases not working properly under SIA. Basically I'll try to map it to a relative frequency problem, where all the possibilities are realised a large but finite number of times, and count P[E] as the relative frequency of observations which contain evidence E (including any indexical evidence), taking the limit where the number of observations increases to infinity. I'm not totally satisfied with that approach, but it seems to work as a calculational tool.