Envelopes of conditional probabilities extending a strategy and a prior probability

Any assessment formed by a strategy and a prior probability is a coherent conditional probability and can be extended, generally not in a unique way, to a full conditional probability. The corresponding class of all extensions is studied and a closed form expression for its envelopes is provided. Subclasses of extensions meeting further analytical properties are considered by imposing conglomerability and a conditional version of conglomerability, respectively. Then, the envelopes of extensions satisfying these conditions are characterized.