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: $E_{set}(variable)$...