Odds of Getting In
The odds of getting in at the very ground level is 100%. You won't be turned away from an open mic. Your odds go down slightly in terms of securing paid gigs, although if you stick with it long enough, someone is bound to give you a chance.
But if you're actually interested in making this your career and not just a hobby, your odds are abysmal. Which is fine, because you can simply channel all of your failure and misery into your work.