Abstract We consider a new definition of conditional events, useful for their algebraic treatment and for the study of their relations. After we introduce the new concept of fuzzy event as a generalization of the one of conditional event and we define a “weight function” on the fuzzy events, called also “finitely additive probability” that generalizes the finitely additive probability on conditional events. Finally, by generalizing the “bet criterion” of de Finetti, we construct some particular finitely additive probabilities on fuzzy events that are extensions of finitely additive probabilities on conditional events.