1. Very likely or probable. Judging by the FBI's activity around the building, it seemed odds-on that an arrest would be made soon. It's odds-on at this point that we'll have to liquidate the company.

2. Most favored to win in a race. (Used almost exclusively in the phrase "odds-on favorite.") As usual, Man o' War is the odds-on favorite to win. I'd say no other horse really stands a chance. Who do you think is the odds-on favorite to win the World Cup?