When the probability of an event is defined in the "universe" or sample space of all possible basic events, the probability must satisfy the following Kolmogorov axiom. In other words, probability can be interpreted as a measure defined on σ algebra of subsets of sample space, and those subsets are events, so the measures of all sets are. This property is very important because the natural concept of conditional probability is put forward here. For each non-zero probability a, another probability can be defined in space: this is usually read as "the probability of b given a". If the conditional probability of b is the same as the probability of b given a, then A and B are said to be independent. When the sample space is finite or countable, the probability function can also define its value through basic events, here.
For specific explanation, please refer to the following documents.
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