Definitely agree on the first point (although, to be careful, the probabilities I assign to the three events could be epsilons apart if I were convinced of a bidirectional implication between 1 and 2).
On the second part: Yep, you need to start with some prior probabilities, and if you don’t have any already, the ignorance prior of 2^{-n} for each hypothesis that can be written (in some fixed binary language) as a program of length n is the way to go. (This is basically what you described, and carrying forward from that point is called Solomonoff induction.)
In practice, it’s not possible to estimate hypothesis complexity with much precision, but it doesn’t take all that much precision to judge in cases like Thor vs. Maxwell’s Equations; and anyway, as long as your priors aren’t too ridiculously off, actually updating on evidence will correct them soon enough for most practical purposes.
Definitely agree on the first point (although, to be careful, the probabilities I assign to the three events could be epsilons apart if I were convinced of a bidirectional implication between 1 and 2).
On the second part: Yep, you need to start with some prior probabilities, and if you don’t have any already, the ignorance prior of 2^{-n} for each hypothesis that can be written (in some fixed binary language) as a program of length n is the way to go. (This is basically what you described, and carrying forward from that point is called Solomonoff induction.)
In practice, it’s not possible to estimate hypothesis complexity with much precision, but it doesn’t take all that much precision to judge in cases like Thor vs. Maxwell’s Equations; and anyway, as long as your priors aren’t too ridiculously off, actually updating on evidence will correct them soon enough for most practical purposes.
ETA: Good to keep in mind: When (Not) To Use Probabilities