I'm not sure how I can explain this any better... but what you are saying is just wrong. I thought the examples I've written would help you see the light, but so far, no such luck. Maybe I should think about this some more and post again when I can come up with a different way of explaining this.
Ok, how about this............:
1. Let's simplify this: Let's just talk about the Ac. I'm confident that with 20 cards being dealt to 10 players preflop, you will agree that the odds of the Ac being in play is 20/52=38%. Right? Now let's substitute that information into this quote of yours, fixing it to match our new scenario (I'll bold what I'm changing, and I'm cutting out the middle part that is irrelevant):
Old scenario:
New scenario:
CLEARLY, our new scenario is incorrect. I mean, the Ac is ON THE BOARD, so we know it's not in someone's hand, but using your logic, you would have me believe that there is a 38% chance that someone is also holding it. And that's obviously wrong. Agreed?
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