We introduce the definition of a conditional possibility (and a conditional necessity by duality) as a primitive concept, ie a function whose domain is a set of conditional events. The starting point is a definition of conditional event E|H which differs from many seemingly “similar” ones adopted in the relevant literature, which makes the third value depending on E|H. It turns out that this function t(E|H) can be taken as a conditional possibility by requiring “natural” property of closure of truth-values of the conditional events with respect to max and min. We show that other definitions of conditional possibility measures, present in the literature, are particular cases of the one proposed here. Moreover, we introduce a concept of coherence for conditional possibility and a relevant characterization theorem, given in terms of a class of unconditional possibility measures.