This horse in all honesty didn't have a snowball's chance in hell of winning.
(*) a chance in a million(*) a chance worth taking(*) a chance of success(*) a chance of a lifetime
“When hell freezes over” is a related idiom. The meaning is slightly different, but close.
Trivia:
There is an album by the band Eagles named “Hell Freezes Over”. The Eagles had broken up. When one of the members was asked if they would ever get back together, he replied “When hell freezes over” meaning there is NO chance of it happening. However the band did get back together, so they called their next album When Hell Freezes Over.