Legal Probabilism is the view that mathematics, and probability theory in particular, can be used to explicate the standard of legal decisions. While probabilistic tools are sometimes used in courtrooms, the construction of a general model of evidence evaluation remains a challenge. Conceptual difficulties facing Legal Probabilism include the difficulty about conjunction, the difficulty about corroboration and the gatecrasher paradox. These problems need to be addressed before we construct a general model. In this survey we discuss the three difficulties and present some theories proposed as their solutions.Małgorzata Stefaniak, Rafał Urbaniak