Annie is on the 99th floor of a building with 100 stories. There is one elevator in the building, which always travels all the way to the 100th floor before going back down and all the way to the 1st floor before going back up. It stops at every floor for exactly 10 seconds and it takes 5 seconds to travel between floors. When Annie walks up to the elevator, it is not on her floor. What is the probability that the first time the elevator stops at her floor, it will be going down? Express your answer as a common fraction.