I'll be really glad if you respond to this question. I am working with an interesting probability calculation problem. In my problem there are ratings for 32 chess players. They are divided into two groups to form two chess teams in such a way that each team contains all types of players. However, each team should contain only 4 players and the whole design for selecting the players for the two teams has been made according to the diagram attached with this question (which is very important to see how the design goes).

32 players are randomly divided into two groups first, each containing 16 players. Each of these 16 players are further randomized into 4 groups each containing 4 members. Then within each group, the players are arranged in ascending order of their ratings. Then the players with lowest rating in the 1st group, 2nd lowest in the 2nd group, 3rd lowest in the 3rd group and highest in the 4th group are selected to from a team.

Given this design, what is the probability that player i, (i=1,...,32) will be assigned to Chess Team-1? (Please see the attached image to have a better understanding!)