Repetition Probability of Matching items

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There are 64 pieces of paper laid out from 1 to 64. 64 other pieces of paper identically marked are randomly picked from a bin and assigned to the original 64 pieces of paper at random (does not have to be assigned to the same number but each original number can only accept one number). Without replacing a picked piece of paper and picking pieces of paper from the bin till none are left, what is the probability of both papers marked 1 being put together?