A standard deck of 52 playing cards is well shuffled and drawn 1 card at a time without replacement. What is the probability that the ranks of the 3 most recently drawn cards (starting at drawn card 6) have already been seen in the exact same order in the already drawn cards? For example, when the 6th card is drawn, we need to check if cards 4, 5, and 6 are the same exact ranks as cards 1, 2, and 3 in the same exact order. If not, then we draw card 7 and check if cards 5, 6, and 7 have been seen in that same order in cards 1, 2, 3 or 2, 3,and 4... So basically we are checking the last 3 cards drawn against all previously drawn triples, including overlapping triples (such as cards 2,3,4 that overlap cards 1,2,3)
So for example, using A, 2, 3, 4, 5, 6, 7, 8, 9, T, J, Q, K as the 13 possible card ranks, the following partial deck would be a pattern found scenario:
5, Q, 7, 3, K, K, 8, Q, 7, 3 because the Q, 7, 3 triple was previously seen in that exact order.
$UPDATE$: For clarification, you need not scan into the last 3 cards drawn for a match. When I said overlapping triples I did not mean into the last 3 cards drawn, but rather overlapping triples such as scanning cards 1,2,3 then 2,3,4, then 3,4,5... from the last 3 cards drawn (start scanning after card 6 is drawn and after every other drawn card after that such as 7, 8,... 51, 52).
So my question is what is the probability this will happen at least once in a well shuffled deck? That is, at least one triple pattern of ranks will repeat exactly in order in the same deck as the cards are drawn one at a time, as described above.