  The violation of Bell inequalities is often interpreted as showing that, if
hidden variables exist, they must be contextual and non local. But they can
also be explained questioning the probability space employed, or the validity
of the Kolmogorov axioms. In this article we explore the additional constrains
which can be deduced from two widely used objetive probability theories:
frequentism and propensities.
  One of the strongest objections in the deduction of one version of Bell
inequalities goes about the probability space, which assumes the existence of
values for the output of the experiment in each run, while only two of the four
values can be measured each time, making them counterfactual. It is shown that
frequentism rejects the possibility of using counterfactual situations, while
long-run propensities allow their use. In this case the introduction of
locality and contextuality does not help to explain the violation, and an
alternative explanation could point to a failure of the probability.
  Single case propensities were designed to associate probabilities to single
events, but they need to be conditional to the whole universe, and do not have
a clear link with the observed relative frequencies. It heavily limits their
use.
