  There exist several phenomena (systems) breaking the classical probability
laws. Such systems are contextual dependent adaptive systems. In this paper, we
present a new mathematical formula to compute the probability in those systems
by using the concepts of the adaptive dynamics and quantum information theory
-- quantum channels and the lifting. The basic examples of the contextual
dependent phenomena can be found in quantum physics. And recently similar
examples were found in biological and psychological sciences. Our novel
approach is motivated by traditional quantum probability, but it is general
enough to describe aforementioned phenomena outside of quantum physics.
