The Nationwide Basketball Society (NBS) has 8001 teams, numbered 2000 through 10000. For each n, team n has n+1 players, and in a sheer coincidence, this year each player attempted n shots and on team n, exactly one player made 0 shots, one player made 1 shot, \ldots, one player made n shots. A player’s field goal percentage is defined as the percentage of shots that the player made, rounded to the nearest tenth of a percent. (For instance, 32.45 \% rounds to 32.5 \%.) A player in the NBS is randomly selected among those whose field goal percentage is 66.6 \%. If this player plays for team k, what is the probability that k \geq 6000?