Yes, I suppose it means conditional on the event \”Y=8\”. I have updated the answer here. Usually, parentheses or curly brackets should be used to indicate the event. Here it is doing this in a very informal way.
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Oh wait, I think maybe it means conditional on the event “Y=8″… it should have parenthesis like X|(Y=8). This is very informal. I will update the answer in a few minutes.
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Honestly speaking, I don’t see how “X|Y = 8” refers to the existence of S. There is no S involved. There are usually two ways of interpreting the operation |. One is “conditional on the latter, ” but it doesn’t make any sense here. Another is “divisibility”, like “2|4” means 4 can be divided by 2. Neither makes any sense here, so there is no way I am able to fix this.
