I've often felt that one of the reasons such warnings are even necessary, is because the notation we use to denote probabilities in the first place is atrocious

I've often felt that one of the reasons such warnings are even necessary, is because the notation we use to denote probabilities in the first place is atrocious, and clearly an abuse of notation. A better convention would make clear the distinction between the set of possible outcomes, the act of obtaining a (range of) samples from that set, and the probability that those events match a value range of interest. p(x=X) is not enough to capture all that information. let alone p(x) vs p(X).