  Drawing from the optimal transport theory adapted to the relativistic setting
we formulate the principle of a causal flow of probability and apply it in the
wave packet formalism. We demonstrate that whereas the Dirac system is causal,
the relativistic-Schr\"odinger Hamiltonian impels a superluminal evolution of
probabilities. We quantify the causality breakdown in the latter system and
argue that, in contrast to the popular viewpoint, it is not related to the
localisation properties of the states.
