I wanted to be an NBA basketball or professional basketball player in Europe, but after a below average college basketball career it was not a realistic option and I knew it wasn't realistic even in high school. I then wanted to be a police officer and was in the process of the backgrounds etc, which can take up to two years. I was working as a paralegal out of college and decided to take the LSAT expecting to do terribly. I did pretty well and was then offered a number of scholarships and I thought why not go to law school with a scholarship I did not have much to lose. In all honesty I really thought I would fail out, but my background for to be a police officer woudl be done by then and I would go back to that.
I ended up finishing in the top 10% of my class, which was a complete surprise to me and ended up loving law school and being a lawyer, but for the first 24 years of my life I thought there was no way I would ever be a lawyer, but it happened.
I think every story is unique and since law school does not require pre-req courses like med school it results in a lot more diverse backgrounds.