Subjective time and self-locating probability

Suppose I am sluggish mentally in the morning and function fast mentally in the afternoons. I find myself in a dark room with no information about what time it is. Consider the two hypotheses MORN, that it is between 7am and 8am and AFT, that it is between 1pm and 2pm. Which is more likely, or are they equally likely?

It seems obvious that if I function mentally the same way in the morning and afternoon, MORN and AFT should be equally likely.

But now suppose I live in a world where every morning all processes in the solar system slow down by a factor of two, returning to the normal speed in the afternoon. Then, surely, for all practical purposes, the period from 7am to 8am is half an hour long! And so it seems right to say P(MORN) = (1/2)P(AFT). But the case of my own mental sluggishness seems to be just a more localized version of the solar system slowing down. Thus, in my original story we should say that likewise P(MORN) < P(AFT).

Here is one way to imagine mental functioning slowing down: my thinking is divided into discrete moments (like a computer’s internal clock, where basic operations take a clock cycle), and in the morning there are fewer of these discrete moments of thinking. If so, then it seems reasonable to say that the probability that the current time is between x and y is proportional to the number of discrete moments of thought between x and y, and hence P(MORN) < P(AFT), there being fewer moments of thought in the morning.

But I have a hard time getting good intuitions about the continuous case.