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I know that this is a very general question but I'm struggling to understand.. What does this probability notation mean?

$Pr_{set}(event)$

This should be the probability over some set, but what does it mean to calculate the probability over a specific set? I mean, the probability should be of an event, so how could it be in respect to different sets?...

For example, I encountered it here in the wiki article about universal hashing: https://en.wikipedia.org/wiki/Universal_hashing#Mathematical_guarantees

$$Pr_{h\in{H}}(h(x) = h(y))$$

Same question for the similar notation of expected value in respect to a set: $E_{set}(variable)$...

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    $\begingroup$ Not familiar with the notation, but maybe $P_{S}(A)=P(A\mid S)=P(A\cap S)/P(S)$? Defined like this $P_S$ is a probability measure. $\endgroup$ – drhab Aug 30 '19 at 8:41

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