I think that it's a mistake to reserve the term ‘probability’ for beliefs held by actual people (or other beings with beliefs). In fact, since actual people are subject to such pervasive epistemic biases (such as we try to overcome here), I doubt that anybody (even readers of Less Wrong) holds actual beliefs that obey the mathematical laws of probability.

I prefer to think of probabiliy as the belief of an ideal rational being with given information / evidence / observations. (This makes me what they call an ‘objective Bayesian’, although really it just pushes the subjectivity back to the level of information.) So even if nobody knows the frequency with which a given coin comes up heads (which is certainly true if the coin is still around and may be flipped in the future), I can imagine a rational being who knows that frequency.

But in a post that was supposed to be pedantic, I was remiss in not specifying exactly what information the probability depends on!