Odds of Getting In
Low. The best firms have a line a mile long begging to be hired. The firms generally like insecure people who need the work to feel good about themselves. Consultants are famously good at recruiting. They present marvelous career paths and intellectual curiosities to be sated on the fields of business battle.
Think about what it likely took to become a senior player at one of the major consulting firms. Enormous sacrifice of family and personal life. Not everyone would be willing to do that. It's likely that they want to hire younger versions of themselves because then they can be sure that they've got a good employee who won't abandon the company in favor of becoming a stay-at-home dad.
If you're willing to travel endlessly for very nice but not Wall-Street-amazing money, with a job that is forever intellectually stimulating, then study hard, get into a top tier school, and go for it. Consulting is a great gig if it fits your personality.