Why did harry just not use the pensieve to prove sirius black's innocence in the third film?

For starters, the pensieve didn't appear until Goblet of Fire. Also, the pensieve doesn't just show everybody's memories. It only shows memories that have been put in it. Nobody ever took the memory and put it in the pensieve, therefore the pensieve could not show it. Of course I don't know how anybody who has never read the books understands the movies AT ALL. They leave out way too much.