Probabilities are a philosophical rat's nest of sorts. When it comes to statistics, it's generally agreed that we're working with a frequentist interpretation of the meaning of probabilities, but you are right that a person with no prior background could well have a completely different understanding here (subjectivist probability, degrees of belief).

I also think stating presuppositions and limitations around observation and prior knowledge is monumentally important as soon as you begin talking in terms of probabilities, if you really want your statements to be clear, but most people don't do this. There are some ways in which I think the casual use of probabilities can actually be more harmful than encouraging a simple binary boolean dichotomy of "I know" or "I don't know" and need more information.