Assuming we escape the null space of solipsism, and can reason about anything at all, we can think about what a model might look like that generates some ordering of P(#). Of course, without a hypothetical consciousness detector (one might believe or not believe that this could exist) P(#) cannot be measured, and therefore will fall outside of the realm of a scientific hypothesis deduction model. This is often a point of contention for rationality-pilled science-cels.
Some of these models might be incoherent - a model that denies P(#1) doesn't seem very good. A model that denies P(#2) but accepts P(#3) is a bit strange. We can't verify these, but we do need to operate under one (or in your suggestion, operate under a probability distribution of these models) if we want to make coherent statements about what is and isn't conscious.