The question is "Do you all want a drink?" They're all answering with the logical meaning of "all", where it's yes if and only if every single one of them wants a drink, not the common meaning. Their responses are the value of the predicate `(A wants a drink) AND (B wants a drink) AND (C wants a drink)`.

If either of the first two didn't want a drink, they would be able to answer "no". They each started off knowing one of the terms in that logical AND above. (They know their own preferences are either "yes" and "no" but they aren't yet aware of the others' preferences, and they each know the others know that.)

For example, if (A wants a drink) is false, then the whole predicate is false. So if A didn't want a drink, A would've said "no". But instead they say "I don't know". They could only have not known if they actually do want a drink but are unsure whether both of the others also do. But after the first two people each say something that reveals they do want a drink, the third person "C" knows that:

1. A wants a drink (or they would have said "no")

2. B wants a drink (or they would have said "no")

3. C wants a drink (knowledge of their own preferences)

and finally has enough information to conclude that the overall predicate is true.