Conditioning on MV-Algebras and Additive Measures, Further Results

In probability theory the conditional probability of an event a given an event b is introduced as the normalized (ordinary) probability of a, restricted to the (fixed) subuniverse b, i.e. as the quotient \(\frac{{m(a \cap b)}}{{m(b)}}\) for m(b) > 0, and can be interpreted as the ‘(probability of a) given b’ rather than as ‘probability of (a given b)’, because such conditional events ‘a given b’ were not defined.