Does "odds-on favourite" mean more than 50% chance?

You forgot to include in your question your own research on odds-on, which was clearly consistent with (for example):

Odds-on = having or viewed as having a better than even chance to win “the odds-on favorite”

Merriam Webster

The odds are the ratio of one outcome to the others. For example:

Odds. Ratios of probabilities, they can be defined in two different ways: odds in favor of an event ("odds on") or against an event A ("Odds Against). Odds can be expressed as a ratio of the probability an event will happen divided by the probability an event won't happen: Odds in favor of A = A / (1 - A), usually simplified to lowest terms., For instance, if the probability of an event occurring is 0.75, then the odds for it happening are 0.75/0.25 = 3/1 = 3 to 1 for, while the probability that it doesn't occur is 1 to 3 against.

Data science

With all this in mind it is clear that the odds-on favorite has a better than even (more than 50%) chance of winning, leaving less than 50% chance of winning to any or all of the others. There can therefore be only one such odds-on favorite.

This negates your second option.