When there exists uncertainty, AI machines are designed to make decisions so as to reach the best expected outcomes. Given that such expectations are based on the true facts about the objective environment with which those machines interact, these facts can be encoded into the AI models as a form of true objective probability function. Therefore, such AI models involve probabilistic machine learning whose probabilities are objectively interpreted. We prove under some basic assumptions when machines can learn the true objective probability, if any, and when machines cannot learn it.