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After reading this thread, I remembered that Liar Game basically did this concept but with two cards instead.
I think people get confused over the fact that you've already picked out the green ball and thus there is no other option, but I think it's similar to pic related where if you pick out the red ball you restart the whole box picking procedure again.
Meaning that since you've already picked out a green ball there is a "higher" chance of there also being a green ball in the same box, just from the fact you HAVE a green ball in your hand.
At least that's how I'd see it. I'm probably wrong in this line of thinking.