If the first two didn't want a drink, then they would have known that they did not ALL want drinks. So they would've said no.

The first one wants a drink, but she doesn't know if the others do. The second one wants a drink. He knows the first one would've said "no" if she, personally, didn't want a drink. He also says no. The third one wants a drink. You'll be surprised to hear this, but xe is also aware that One and Two would've said "no" if they, personally, didn't want a drink. So Xe deducts that all three of them want drinks.