Summary: We introduce a generalization of \(\varepsilon\)-probability functions and a new correspondence with rational consequence relations. The rational consequence relations corresponding to the generalized \(\varepsilon\)-probability functions of maximum entropy are investigated, and it is shown that in this case the analogous notion of ‘maximum entropy closure’ equals the rational closure, thus reconfirming the rational closure of a conditional knowledge base as the simplest, least prejudiced, rational consequence relation satisfying that knowledge base.