Let Ω be the sample space of all possible outcomes let P(A) denote the probability of event A, define the set of all probabilities: S = {x | 0 ≤ x ≤ 1} and the set of all non-probabilities:

S' = (-∞, 0) ∪ (1, +∞)… for any event A:

P(A) ∈ S

1 - P(A) ∈ S

now if we know S', we can determine S, and thus all probabilities. By defining the set of all non-probabilities (S'), we effectively create a boundary for all valid probabilities. Any number not in S' must be a valid probability. This allows us to predict all probabilities by knowing what they cannot be. "A set of all non-probabilities" is correct because it provides a complete definition of what probabilities are not, thereby allowing us to deduce all valid probabilities…

Source: x.com/BLUECOW009/status/1847659061614895319