I've referenced the idea of the interpretation of probability a number of times over the years. This article, newly revised, describes the concept. An 'interpretation' of a statement like 'Rome will probably fall some day' describes what we mean when we say such a thing. It could reference "an epistemological concept, which is meant to measure objective evidential support relations... (or) an agent's degree of confidence, a graded belief... (or) a physical concept that applies to various systems in the world, independently of what anyone thinks." Any formal system will require an interpretation, which is why there is an inherent subjectivity in the use of such systems.
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