Yes, it absolutely is an open question, as can be seen in applications in quantum mechanics.
Like Unitarity, and challenges to it - though I am inclined to think they are definitional (along Cartwright's 'How The Laws Of Physics Lie' lines) rather than epistemic.
And the expanded probability ensemble, as briefly discussed in a question here with links, though sadly not answered yet https://physics.stackexchange.com/questions/11049/does-the-extended-probability-ensemble-interpretation-of-quantum-mechanics-make
Electron orbitals seem to have negative probabilities. This is a bit deceptive, because they only do so relationally, when a paired electron is there with opposite spin, yet somehow preserving in the total state that one electron is less likely to be where it's orbital partner is than located at the nucleus (because this wave-like behaviour is captured in the imaginary part, lost in observations).
Like entropy, we feel with probabilities we grasp an absolute, an intrinsic quality of a system, but find in practice it is often, usually, relative, about a change between ststems rather than absolute terms from first principles - reality, and useful conceptualisation/abstraction, is often too complex for that, and toy systems lead us to over-optimism.
Investigating the deep meaning of probabilities is key to future physics. The transition between fermions and bosons responsible for superconductiin & superfluidity for instance. Blackholes are now thought to be a (bosonic) superfluid that has an absolute maximum of entropy for a given volume. Penrose's Conformal Cyclic Cosmology seems to equate a pure photon soup to the opposite, a white hole. Somehow the transition between these (ie, a timeline including both the big bang, a white hole, and evaporating blackholes) has to either preserve entropy increase, and conservation of information, or show how these can be violated. These heuristics are the deepest principles of our understanding of the world, and we know there is an inconsistency. A better understanding the true implications of probability is clearly key to resolving this.