Final answer:
The train operator would notice a third rail power failure during braking when the train doesn't decelerate as expected, or when there is a loss of control in the braking system, accompanied by failures in the train's electrical systems such as lighting.
Step-by-step explanation:
While a train is braking at a passenger station, if third rail power fails, the train operator would surely become aware of this failure when the expected deceleration doesn't occur or is less than anticipated. This is because third rail systems provide the electrical power necessary for a train's propulsion and other functionalities. Without power, the train would lose the ability to actively brake using its electrical systems, which could potentially result in the emergency brakes being automatically activated, or the operator noticing a loss of control or responsiveness in the braking system. Additionally, the train's interior lighting, announcements, or other electrical systems may fail, which would also alert the operator to the power loss.