Question: X is (continuously) uniformly distributed over an interval ([a, b]), and (M subset[a, b]) is a disjoint union of intervals whose widths sum up to

X is (continuously) uniformly distributed over an interval $[a, b]$, and $M \subset[a, b]$ is a disjoint union of intervals whose widths sum up to $w$. What is $P(X \in M)$ ?

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