Analogical proportions are relations that link 4 items a, b, c and d and that are expressed as “a is to b as c is to d”. These 4 items are often described by vectors of Boolean, nominal, or numerical values. Analogical proportions can however relate logical formulas. The article proposes a first study of analogical proportions between probabilities, whether they are simply between values, or between distributions (which requires the preservation of their normalization). The properties of definitions based on arithmetic proportion, or combining the latter with geometric proportion are studied, and potential uses are described. An appendix proposes a proof of the Pythagorean theorem in terms of geometric proportions.