Mursalin likes to collect playing-cards. In fact he has \(1374\) decks of playing cards. One day he decides to take all of his decks and places them in a row on a (big!) table. He randomly takes out one card from the **first** deck and places it somewhere inside the **second deck**. Then he takes a random card out of the **second** deck and places it somewhere inside the **third** deck. He keeps on doing this with the other decks. He repeats the process until he takes out a random card from the \(1374^{\text{th}}\) deck and there aren't any more decks left. The probability that the last card selected is an ace can be expressed as \(\frac{a}{b}\) where \(a\) and \(b\) are co-prime positive integers. What is \(a+b\)?

**Details and assumptions:**

A regular deck of playing cards has \(52\) cards \(4\) of which are aces.

The image is taken from here.

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