Bob runs a snow cone stand, and customers go in and out by an M/M/1 queuing system model. Bob's average service time is 0.5 minutes for one customer. (You don't need the arrival rate to answer this question.)

Alice gets in line and is the 4th customer in line.

Due to the ongoing the friendly rivalry between Alice and Bob, Alice challenges Bob's service speed with the following wager:

If after 1 minutes, Alice is still in the system, then Alice wins.

But if Alice gets out before spending 1 minutes total in the system, then Bob wins.

What is the chance that Bob will win the wager? Give the probability in decimal form, rounded to 3 places.