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Yes, both probabilities are zero.
In practice, creases are not infinitely thin so I think the probabliity is not 1/∞, but rather some very small fraction that depends on the paper etc.
Say you have identical sheets of paper, and you take one sheet and make a random crease in that sheet of paper, what is the probability that if someone else folds a random crease in one of the other sheets that it will be the exact same crease. I figured it would be 1/infinity, but what If the second person was allowed to make 5 random creases in the second sheet what would the probability that 1 of those creases was identical to the original crease... 5/infinity?