Mathematical proofs are often complex and hard to verify by their readers. Consequently, the application of formal proof systems are a useful approach in the area of verification. We present a framework for computer proofs in probability theory. Therefore we describe formalized probability distributions and fundamental lemmata concerning σ-algebras, probability spaces and conditional probabilities. These are given in the formal language of the formal proof system Isabelle/HOL. Besides we describe an application of the presented formalized probability distributions and fundamental lemmata to cryptography. Our achievements are a step towards computer verification of cryptographic primitives. They describe a basis for computer verification in probability theory for interactive proof constructions within the formal proof system mentioned above. Computer verification can be applied to further problems in cryptographic research, if the corresponding basic mathematical