Surely. You just need to make some prior on the 3rd. Note, that the 3rd hypothesis is something along the lines of “there is some other model besides Boltzmann hypothesis or Boltzmann brain”, not a specific hypothesis. It can be big bang, god created the universe, or we live inside simulation. Whatever.
Now, you would have to assign unreasonably small prior to this for it not to end up many orders of magnitude more probable than either of Boltzmann Hypothesis or Brain.
Can we estimate the probability of this 3rd hypothesis or even compare it with the probability of the other two?
Surely. You just need to make some prior on the 3rd. Note, that the 3rd hypothesis is something along the lines of “there is some other model besides Boltzmann hypothesis or Boltzmann brain”, not a specific hypothesis. It can be big bang, god created the universe, or we live inside simulation. Whatever.
Now, you would have to assign unreasonably small prior to this for it not to end up many orders of magnitude more probable than either of Boltzmann Hypothesis or Brain.