When six basketball players are about to have a free-throw competition, they often draw names out of a hat to randomly select the order in which they shoot. What is the probability that they shoot free throws in alphabetical order? Assume each player has a different name. $\mathrm{P}$ (shoot free throws in alphabetical order) = (Type an integer or a simplified fraction.)

Step 1 ：The total number of ways to arrange 6 players is 6 factorial (6!). This can be represented as \(6!\).

Step 2 ：There is only one way to arrange the players in alphabetical order.

Step 3 ：Therefore, the probability of the players shooting in alphabetical order is \(\frac{1}{6!}\).

Step 4 ：Final Answer: The probability that the six basketball players shoot free throws in alphabetical order is \(\boxed{\frac{1}{720}}\) or approximately \(\boxed{0.00139}\).