It is shown that the probabilistic organization of quantum mechanics involves a tree-like structure which we have called "the probability-tree of a state preparation." Though this construct emerges by systematic reference to the abstract theory of probabilities as it now stands, it transgresses this theory. The quantum mechanical transformation theory is found to concern implicitly a type of probabilistic dependence that is not defined inside the nowadays theory of probabilities, namely a probabilistic metadependence via a common monolith of potentialities, between globally considered probability measures from distinct probability spaces belonging to one same tree. The principle of superposition is found to concern a certain type of probabilistic meta-metadependence between distinct trees. So, when it is referred to the nowadays abstract theory of probabilities, quantum mechanics, via its organization in probability trees, appears as neither a "normal" probabilistic theory, nor an "abnormal" one, but as a pioneering application of a possible future, extended abstract theory of probabilities.