Odds of Getting In
New talent is always arriving on the scene and hitting it big, so there's always a call for new personal assistants. If you network like crazy, get yourself signed up with an assistant temp agency, and develop a résumé and referral list that shows you're willing and able to roll with the punches (both figurative and literal), you should be able to get your foot in the door with some celebrity.
Your chances may be better if you spend some time first getting assistant work in the entertainment industry, like in a talent agency or a production studio. Many of the skills you pick up there will translate, and you'll have an idea what the other facets of your boss's business is like (source).
It'll also get you used to being bossed around all the time, just in case your parents didn't already take care of that one for you.