Good ol' Probability

For the probability to be 1 in 52!, you need to specify that the first 13 cards are all of one particular suit, then the next 13 cards of all of anothe particular suit, etc., so that there is only ONE array of cards that "meets the criteria". Otherwise, the probability is going to be a lot less than 1 in 52! . For instance, suits don't matter at all, even in any block of 13 cards, then the probability is 1 in 52! divided by 4!^13.

If you look at a deck then there are 52 cards in total, so let's take this one step at a time. Now, as the problem asks, what are the chances that the king would be first. Since it isn't specified which king should be first, then we can just assume that a king would take that place and every other card would go in order 4x all the way to one. If that is the case then, the first card should have the probability of $\frac{1}{52}$ and seeing that this position is taken then the next position would be multiplied by the previous as $\frac{1}{51}$ and so on like so, if you remove the 1's for simplicity.

52 x 51 x 50 x 49...... x 1

Which would give you the mind-bogglingly, I know that isn't a word , large number of 52! or 52 factorial. This number can be shown as 8.06x10^67. This number is so large that you would need a whole video to explain it, which is why you should watch this. (https://www.youtube.com/watch?v=0DSclqnnC2s)