Introduction:
In this problem, we are given that cards are thoroughly shuffled and distributed equally among four players. We need to find the probability that a specific player gets all four kings. Let's solve this problem step by step.

Step 1: Find the total number of ways to distribute the cards:
To find the total number of ways to distribute the cards, we need to calculate the number of ways to arrange the 52 cards in a deck. Since the cards are distributed equally among four players, each player will receive 13 cards. Therefore, the total number of ways to distribute the cards is given by:

Total number of ways = (52C13) * (39C13) * (26C13) * (13C13)

Here, "nCr" represents the combination formula, which calculates the number of ways to choose "r" objects from a set of "n" objects.

Step 2: Find the number of ways the specific player gets all four kings:
Since there are 4 kings in a deck, the specific player can only get all four kings if we choose those four kings for that player. Therefore, the number of ways the specific player gets all four kings is given by:

Number of ways = (4C4) * (48C9) * (36C13) * (23C13) * (10C13)

Here, we choose the four kings for the specific player, and then choose the remaining cards for the other players.

Step 3: Calculate the probability:
Finally, to calculate the probability, we divide the number of ways the specific player gets all four kings by the total number of ways to distribute the cards:

Probability = Number of ways / Total number of ways

Conclusion:
In this problem, we calculated the probability that a specific player gets all four kings when cards are thoroughly shuffled and distributed equally among four players. By dividing the number of ways the specific player gets all four kings by the total number of ways to distribute the cards, we obtained the probability.