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.
The bartender asked if all of them wanted a drink.
Logician number one does not know whether logicians number two and three want a drink or not, so he can’t say yes. If he did not want a drink though, he could say no because then it would not be true that they all wanted a drink. But he wants a drink. Therefore he says he don’t know, because it will depend on whether the other two want drinks or not.
Same applies to logician number two. She is still missing info about the third logician and therefore says she doesn’t know.
The third logician now knows that both of the other two want drinks, and so can answer that all of them want drinks.
It’s a short circuiting conjunction. Consider `aliceWantsADrink && bobWantsADrink`. If Alice doesn’t want a drink, she knows it’s not the case that both of them want a drink. Since she says “maybe” instead of “no” she signals to Bob that she wants a drink, and so he concludes they both want a drink.
Yes, this was an inappropriate post that has no place here. I'm sorry to the parent poster and anyone whose enjoyment of the joke is blunted by this. I certainly didn't intend to be an insulting downer but I certainly don't expect anyone to read it as anything but intending to insult. I apologise.
Three philosophers walk into a bar, and the bartender asks: "Do you all want a drink?"
The first one says "I don't know."
The second one says "I don't know."
The third one says "Yes!"