  Kolmogorov's axioms of probability theory are extended to conditional
probabilities among distinct (and sometimes intertwining) contexts. Formally,
this amounts to row stochastic matrices whose entries characterize the
conditional probability to find some observable (postselection) in one context,
given an observable (preselection) in another context. As the respective
probabilities need not (but, depending on the physical/model realization, can)
be of the Born rule type, this generalizes approaches to quantum probabilities
by Auff\'eves and Grangier, which in turn are inspired by Gleason's theorem.
