What I mean is that those axioms of conditional probability seem intuitively true because of their frequentist interpretation, i.e. counting the possible cases

What I mean is that those axioms of conditional probability seem intuitively true because of their frequentist interpretation, i.e. counting the possible cases that satisfy each probability. If you devoid them from the combinatorics that justify their meaning, there's no special reason to accept these particular axioms nor the law derived from them.