2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/166699We describe a Groebner basis of relations among conditional probabilities in a discrete probability space, with any set of conditioned-upon events. They may be specialized to the partially-observed random variable case, the purely conditional case, and other special cases. We also investigate the connection to generalized permutohedra and describe a conditional probability simplex.20 pages,11 figuresProbabilityAlgebraic GeometryStatistics TheoryMachine Learning60A05; 13P10; 14M25; 52B20text