This is not about someone choosing to lie, it’s about someone choosing what true thing to say. If “you're told that at least one of them is a girl” was intende

This is not about someone choosing to lie, it’s about someone choosing what true thing to say. If “you're told that at least one of them is a girl” was intended to mean “you ask whether at least one of them is a girl and you’re told that at least one of them is a girl” it was pretty easy to make it clear. In that case it’s straightforward that p(you're told at least one is a girl | both are girls) = p(you're told at least one is a girl | only one is a girl) = 1 (with just the mild and reasonable assumption that you’re not being lied to.) Edit: also the reasonable assumption that your question is unrelated to the number of girls - it’s easy to imagine settings where you asked because of something which may be correlated with the number of girls.