The key point is the subject’s relationship to alternative scenarios of how reality may develop.

Both possibility and probability initially presuppose some starting state relative to which alternatives are considered. But they relate to those alternatives differently.

1. Possibility

There is some initial state \\(S_0\\).

The subject distinguishes this state and begins to consider alternative scenarios:

\[ S_0 \longrightarrow \{A_1,A_2,A_3,\ldots,A_n\} \]

In doing so, the subject does not establish which scenario is more probable. The subject allows alternative possibilities that they are capable of imagining.

2. Probability

Now the subject introduces additional distinctions.

For example, initially the subject allows five scenarios. Then they discover some circumstance that makes it possible to assess these scenarios differently.

As a result:

• Some scenarios become more probable.
• Others become less probable.
• Some may be excluded from consideration.
• Some continue to coexist without any definite preference.

It follows that probability represents the subject’s relationship to alternative scenarios in light of additional distinctions that make it possible to assess their relative feasibility.

Note

“This scenario is more probable than another” is a distinction in the modality of possibility, since it does not specify the criteria for such a statement.

Conclusion

Possibility: the subject allows alternative scenarios relative to the initial conditions.
Probability: the subject introduces additional factual distinctions and criteria that make it possible to evaluate alternative scenarios by the degree to which they are supported.

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The following examines a situation in which S0 need not remain static.

3. What Happens to the Initial State?

Here, I think, is the most interesting part of your reasoning.

Both modalities can be considered relative to an initial state that is temporarily taken as given.

But the initial state itself may also become the subject of a new distinction.

Imagine:

The subject has distinguished state \\(S_0\\) and constructed five alternative scenarios.

Then a new distinction \\(D\\) arises.

And now there are two fundamentally different possible outcomes.

First: distinction \\(D\\) allows probabilities to be redistributed among scenarios already under consideration.

Second: distinction \\(D\\) changes how the initial state \\(S_0\\) itself is understood.

In the second case, the subject may discover a scenario that was not among the original alternatives at all. Or discover that the very grounds on which those alternatives were distinguished were different.

This is no longer merely a change in probabilities.

It is a change in the space of possible scenarios itself.

And here an essential distinction emerges between two operations:

1. Making a distinction within a space of alternatives that has already been identified.
2. Making a distinction that transforms the space of alternatives itself.

Moreover, the second operation can change both what was previously considered possible and what was considered probable.

4. Possibility and Probability as Modalities

Your construction can provisionally be formulated as follows:

Possibility is a modality of the subject’s relationship to an alternative scenario in which the scenario is admitted without any need to establish its degree of probability.

Probability is a modality of the subject’s relationship to an alternative scenario in which additional distinctions make it possible to assess its feasibility relative to other scenarios.

Both modalities depend on which distinctions the subject has already made and which initial conditions the subject accepts in the relationship under consideration.

And there is something here that I find particularly interesting.

Probability is not necessarily a deeper knowledge of reality than possibility.

It may constitute a more detailed distinction within an already accepted initial state. But a new distinction affecting the initial state itself can change the entire previous probability distribution.

In other words, one may assess the probabilities of alternatives with great precision while failing to recognize that the very grounds on which those alternatives were identified need to be revised.

This is directly connected to your method of inquiry: a new distinction can not only refine existing alternatives but also change the conditions under which those alternatives arose in the first place.

And then another question emerges: are possibility and probability two modalities of the same relationship, or is probability a derivative relationship that arises after the initial admission of possibility?

Because if the latter is the case, then between them there is not simply a difference, but a definite sequence of cognitive operations.