A probability is a quantified possibility. That
doesn't tell you much about the ontology of probability, because it doesn't tell you much about the ontology of possibility.

A possibility could be a feature of reality, (a propensity) or it could be a merely apparent result of ignorance. (Knightian uncertainty). These are very different theoretically, but hard to distinguish practically.

Concrete examples of real possibilities include MWI branches or metaphysical possible worlds. Neither the meaning nor the usefulness of possibility depends on such realities. Ignorance is always with us, so possibility is always with us.

The quantification of possibility is a separate issue.

Probability is not always with us because it requires the extra element of quantification. Physics supplies no meaning or method for determining the probability of decoherent branches, for all that it is a topic of great philosophical interest.

https://www.lesswrong.com/posts/r282ErRKMFzxpKYMm/can-we-in-principle-know-the-measure-of-counterfactual?commentId=gMFvEMygeT6CTkqMa

If you are interested in the objective probability of the coin flip,the it only has one value because it is only one event. In a deterministic universe the objective probability is 1, in a suitably indeterministic universe it is always 0.5.

The assignment of probability 1 to an event that has happened is also subjective. You don't know that it had to occur with complete inevitability, ie you don't know that it has a conditional probability of 1 relative to the preceding state of the universe. You are setting it to 1 because you are proceeding as if it has occurred. Although determinism is equivalent to the claim that everything happens with probability 1.0, the fact that 1's appear in probability calculations does not imply determinism.

If you think the questions “what will it be” and “what was it” are different, you are dealing with subjective probability, because the difference the passage of time makes is a difference in the information available to you, the subject.

Failing to distinguish objective and subjective probability leads to confusion. For instance, the sleeping beauty paradox is only a paradox if you expect all observers to calculate the same probability despite the different information available to them. The trick is to drop the assumption that there is a "the" probability everyone has to agree on.

The ways possibilities are quantified varies, too. Bayesianism and frequentism are different methods of quantification that often agree. Bayesianism permits a subjective element without excluding objectivity. Frequentist assumptions can be used as priors, and Bayes can converge in frequentist conclusions.

The objective basis of frequentism is the measure of an equivalence class. The objective basis of frequentism is not an objectively existing possibility, ie. frequentism is defineable in a deterministic universe. However , for a measure to be translated into a probability, something has to *happen*. An urn might contain a certain ratio of black balls to white balls , but that is not a (frequentist) probability, until you imagine a ball being drawn at random. Randomness, even imaginary randomness, introduces the necessary element of multiple, non trivial possibilities.

Objective and subjective probability are not mutually exclusive opposites. Strict determinism does not imply any level of information for any observer, so observers can still apply probabilities based on their ignorance of how things turn out

Nobody does nothing but passively make predictions. Agents also change things. That's why they are called "agents", not "patients".