This is the ''white rabbit'' problem which was discussed on this list a few years ago. This can be solved by assuming that there exists a measure over the set of al universes, favoring simpler ones.
I don't believe there are any grounds for assuming that, so the problem isn't solved for me.
Once you consider the whole of Platonia all you have is a probability distribution over the set of all possible states you can be in (because you can't define time in a normal way anymore).
I don't agree with this. I can imagine an infinite 2D lattice of cells, seeded with the binary digits of pi, and ask the following question: if the rules of Conway's Life were applied to this lattice, what would it look like after a million ticks of the clock? There's an objective answer to this question, and that answer exists in Platonia. I believe that this implies that the universe I just described (and all other possible CA universes, and much more) exists in Platonia. I define "time" as the "ticking of the clock" in such computational worlds, so I believe time exists in Platonia. (Of course, in another sense, Platonia exists in a timeless "all at once". This is similar to the way that time exists in the "block universe" of relativity theory.)
There is no conditional probability for your next experience given what you have experienced now. A valid question is: What is the probability that you will be in a state P that contains the memory that you have been in a state P'.
I find this way of looking at things very confusing. What do you mean by "you" in this formulation? Is "you" a thing that jumps from state to state? If so, then we have some form of time. If not, what is this "you"? Obviously it is something that can be said to be "in a state P" (otherwise, you wouldn't consider your above question valid). But what does it mean for "you to be in a state P"? If it's true that "you are in a state P", are you just timelessly in state P, or what? How can you even talk about something "being" without talking about time?