$1374$ 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.