Relative Order

The other five people are irrelevant to the relative ordering of these three.

Among Alice, Bob and Charlie, all $3!$ relative orderings are equally likely.

1. 1. Reduce to three people

   By symmetry, the relative order of Alice, Bob and Charlie within the full line is uniformly distributed over the $3!=6$ possible orderings, regardless of the other five positions.

2. 2. Pick the favorable ordering

   Exactly one of the six orderings is Alice-Bob-Charlie.

   $$P=\frac{1}{3!}=\frac{1}{6}$$

Answer: 1/6