...for example a society which has wizards with similar abilities as in the world of Harry Potter or any D&D magic system - that is, wizards can cast spells to levitate, mind-control and haste the creatures or brew potions to affect their running performance.
In this case the hips ogriffs are not allowed to fly, just run with a rider on their backs.
So what would be the rules and tests to ensure there'd be no cheating?
So the question is, if you'd invent a public entertainment such as hippogriff races, how you'd do it to make it interesting and at the same time ensure the competitors won't get any magical 'assistance' to win?