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We represent knowledge as integrity constraints in a formalization of probabilistic spatio-temporal knowledge bases. We start by defining the syntax and semantics of a formalization called PST knowledge bases. This definition generalizes an earlier version, called SPOT, which is a declarative framework for the representation and processing of probabilistic spatio-temporal data where probability is represented as an interval because the exact value is unknown. We augment the previous definition by adding a type of non-atomic formula that expresses integrity constraints. The result is a highly expressive formalism for knowledge representation dealing with probabilistic spatio-temporal data. We obtain complexity results both for checking the consistency of PST knowledge bases and for answering queries in PST knowledge bases, and also specify tractable cases. All the domains in the PST framework are finite, but we extend our results also to arbitrarily large finite domains.