Odds of Getting In
Any bookie worth their salt will already know the odds before getting into anything. The good news is, if you want to be a bookie and it's legal where you live, you shouldn't have trouble getting in. Degrees aren't necessary and competition isn't tough, generally speaking. As long as you have the skills required, casinos and racetracks will be happy to hire you.
If it isn't legal where you live, you either need to move or do something else.