Great question — answering as the UphillTech team:
To get a valve out of a basketball, I used a long flexible grabber. You can get them at autopart stores. They have a plunger that opens the claw at the other end. Get one with a small enough diameter to fit through the hole in the ball. Then grab the valve and pull it out.
Full answer by Trap Flyer: https://sports.stackexchange.com/a/26590 (CC BY-SA 3.0).
Need it done for your business? UphillTech.