If I have an information I which is true for assumption, is it correct to write both $P(I | I) = P(I)$ or is it always necessary to specify the condition?
2026-05-05 00:37:54.1777941474
Probability notation with and without condition
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From the definition of conditional probability:
$$ P(I|I) = \frac{P(I\cap I)}{P(I)} = \frac{P(I)}{P(I)} = 1 $$
Conditional probability and probability are two different objects so we must be careful with the notation. If you assume that the event I will occur with probability 1, the equality that you wrote is true.