Before revision: More formally: the required change () on c necessary for maintaining logical consistency among the opinions is p(c) = p(a b) which, assuming that a and b are independent events i.e., that p(a b) = p(a) p(b) becomes p(c) = p(a) p(b) + p(a) p(b) + p(a) p(b) where p(a) and p(b) refer to the initial opinions, before the communication induced changes.
After revision: More formally: