  Quantum probabilities differ from classical ones in many ways, e.g., by
violating the well-known Bell and CHSH inequalities or another simple
inequality due to R. Wright. The latter one has recently regained attention
because of its equivalence to a novel noncontextual inequality by Klyachko et
al. On the other hand, quantum probabilities still obey many limitations which
need not hold any more in more general probabilistic theories (super quantum
probabilities). Wright, Popescu and Rohrlich identified states which are
included in such theories, but impossible in quantum mechanics, and they showed
this using its Hilbert space formalism. Recently, Fritz et al. and Cabello
detected that the impossibility of these states can be derived from very
general principles (local orthogonality and global exclusive disjunction,
respectively) without using Hilbert space techniques. In the paper, an
alternative derivation from rather different phyisical principles will be
presented. These are a reasonable calculus of conditional probability (i.e., a
model for the quantum measurement process) and the absence of third-order
interference. The concept of third-order interference was introduced by Sorkin
who also recognized its impossibility in quantum mechanics.
