It is found that Bayes’ law is only a special case of conditional and relational probability where the sample space is invariant. However, in more general cases, the sample space itself is dynamically changing for relational and conditional probabilities.
My thought is it would hold, as long as we have priors for the sequence for events (P(prior) should not be 0). It's just that, as we keep sampling newer and newer data, we will get low probability (close to zero) for unseen events.
Let me add to my answer of probability, which is one of the reference points Bayes' theory. The function of neural networks of the brain based on the fact that the probability of an event, provided that there was another statistically interdependent events. Let me give you another example. Doctors of antiquity did not know Bayes' law. But doctors determined the disease on the basis of detection of a number of symptoms in a patient which (signs) allowed, with varying degrees of probability other features. Professionalism doctor determined experience. Therefore, estimating of computer data handling, it is important to consider the quality of an interface, specific programs, and not only the speed of information processing. Thus, a priori it can be argued that at this stage of knowledge in the computer implementation Bayes' law must take into account the cognitive abilities of the person.
The Bays law is based on conditional probabilities. Whenever these probability are well defined and exist, the law should follow.
You need to construct a probability space to suit your situation. Consult books a measure theoretic probability.
It is just the other way around. If you are working on a complex problem , your formulation should include a construction of a probability space in terms of the functions or other ideas you are working on. Start from a concrete example.
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