A naive definition of knowledge is "justified true belief". To have knowledge, you must believe something. That belief must be true otherwise it is not knowledge. And it must be justified. If your beliefs are true by accident, it is not knowledge.
Edmund Gettier came up with a thought-experiment to criticise this definition. You look through a window and you see your friend Bob sitting with his back to you in an arm-chair. You believe "Bob is in the room". But in fact the figure in the armchair is an effigy, not Bob. However, Bob is in the room, hiding behind a curtain. Your belief is justified and true, but it does not appear to be knowledge. It is true by luck. The justification and the truth are not connected.
The probabilistic view sidesteps the Gettier problem. Beliefs are probabilistic. You see the effigy and you increase your subjective probability that Bob is in the room. But you know you could be wrong. You also believe that the figure in the chair is Bob. You could make bets about it. As it happens, you win the former bet but lose the latter bet. Tant pis.
Relativism is the bizarre view that truths are relative to people, that there is no objective reality regarding certain issues. For example, the belief that a Bob is in the room is true for one person but not for another. This view is rarely thought through by the few who hold it, but probabilism sidesteps it, by clarifying that two people can hold different beliefs based on the evidence they have seen and their priors, but beliefs must be testable by objective reality to qualify as beliefs. Under probabilism, it is meaningless to have a belief you cannot bet on - you need some way of deciding the bet!
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