A large sports tournament is taking place where numerous games of circular dodgeball are played. Each team consists of $6$ players and they can arrange themselves anywhere within a circular boundary during gameplay. Given that the circle's radius is $10$ meters, what is the probability that if a player throws a ball in any direction, it will land within $2$ meters of another player, assuming that the player's location who is throwing the ball is fixed and at the center of the circle?