Imagine that we have a computer program that produces the conscious awareness of the present moment.
Let us assume that every time the program is run a counter is incremented.
Let us also assume that the program is encapsulated in an infinite loop.
Each time the program is run the computer "wakes up" and asks itself "what is the present value of the loop counter?"
The computer reasons that a priori it is equally likely to find itself in any loop with any value of the loop counter.
Therefore the prior probability that the loop counter has any particular value $n$ is $1/\infty=0$.
But the computer will find that it has some loop counter value.
There seems to be a contradiction here.
I think the problem is with the assumption that a computer program can produce conscious awareness in the first place.
I think this argument shows that any deterministic machine cannot be conscious.
Such determinism implies a single-valued time evolution whose (theoretically) infinite extent leads to this zero probability paradox.
I believe to avoid this paradox one needs a branching concept of time in the manner of the many-worlds quantum theory in which each branch into an alternate future is only of finite extent. Maybe the brain itself avoids the paradox by exploiting this many-worlds ontology in its operation.