For example, it implies that, for all a, b and c, P ( a , b ) P ( b , c ) P ( c , a ) = P ( a , c ) P ( c , b ) P ( b , a ) . For example, if we have a Markov chain three states such that only these transitions are possible: A → → B , B → → C , C → → A , B → → A , then they violate Kolmogorov's criterion.