The topic is real world randomness, yes.
The mathematical theory is not in serious doubt. But probability theory has the curious status as having two separate interpretations in the real world - frequentist and Bayesian. In frequentist statistics, a probability is what the fraction of outcomes converges to, for some process that can be repeated an unlimited number of times. In bayesian statistics, a probability is the quantification of belief.
The mathematical manipulation of probabilities is exactly the same, the meanings different.

Does this have to be something actually possible in the real world?