"Once you have discounted the impossible, whatever remains, no matter how improbable, must be the solution."

Sherlock Holmes (A C Doyle)

0 probability = impossible.

(just as an event with 1 probability will always happen)

1/infinity != 0 probability

(though it may be close enough for most observations depending on the accuracy required)

ie the chance of finding your car keys on a beach is close enough to be 0 but is not impossible.

Or the chance someone walks out of a casino with all their winnings, now thats impossible, trust me.