We define algebraic structures which contain all Boolean algebras pseudo-Boolean algebras, and orthocomplenented posets, as special cases; then we introduce the notion of orthonogality and, after defining probability in the usual way, we characterize those among our new structures that admit a full set of probabilities. Some special cases of the main result about characterization are considered and, especially, a result concerning orthocomplemented posets is derived from it. Also, sufficient conditions for the existence of a full set of probabilities on a pseudo-Boolean poset is obtained.