Caption: Venn diagram illustrating what yours truly calls the A-principle and its generalization by Bayes' theorem which is the root of Bayesian analysis.

The Venn diagram makes the A-principle clear.

The contour lines delimit statistical samples (i.e., subsets of the statistical population).

Since sample A is entirely inside sample B, we have conditional probability P(B|A) = 1 which is the A-principle itself.

In words, the conditional probability of B given A is 1. So B exists if A does.

Logically equivalently, P(A|[not B]) = 0.

In words, the conditional probability of A given [not B] is zero---so A does NOT exist if B does NOT exist.