Why is the probability of an event we know happened in a specific problem not equal to 1? [duplicate]

Solution 1:

Here is my question: why is $P(M)≠1$? The problem says $M$ happened.

$\mathsf P(M)$ is not measured under the condition that $M$ happens.   It is the unconditioned probability that $M$ happens.

View it as: how probable we should think it was prior to learning that it was fact.

When we measure probability under a condition, we always indicate that condition.   $\mathsf P(A\mid M)$ is the probability for $A$ under condition of $M$.   AKA the conditional probability for $A$ when given $M$.

When we don't indicate such a condition, the measure does not assume that the condition occurred.