I'm pretty sure I know what's going on here. The question really isn't a puzzle in the sense that's usual here. Rather, it's trying to make a point that's actually applicable in the real world.
When you're asked a question of the form "Here's some information. Now, what's most likely?" two things ought to feed into your answer: (1) what the chances were before you learned the specific information and (2) the impact of that specific information. The first is sometimes called the prior or the base rate.
And it turns out that people very commonly -- not just when answering artificial questions like this one, but in everyday life as well -- forget to take #1 into account because #2 is so much more prominent. This is sometimes called "base rate neglect".
Here's a not-so-artificial example. Suppose you get tested for a Very Rare Disease, and the test comes back positive. It's a pretty reliable test: it only produces false positives 10% of the time. Does that mean there's a 90% chance you have the disease? No! Remember that the disease is very rare. It may well be that even after a positive test result you are much more likely not to have it. (Note: the odds may be different if you are having the test because there are other reasons to suspect you have the disease.)
So, the point of this question -- at least originally, who knows how it may have been being used when you encountered it? -- is to let you discover how seductive base rate neglect is, and then point out that base rate error is a mistake. So you see all those character traits that are somewhat typical of librarians, think "aha, the person is probably a librarian", and then get hit with the observation that actually they're more likely to be a farmer.
Now: is it an absurd question, as the OP suggests in comments? Maybe. Librarians are less common than farmers, indeed. But if you, like (I suspect) many people here, are a middle-class city-dwelling intellectual, then your situation may be like that of the person who gets tested for a rare disease because there's already reason to suspect they have it. There are a lot more farmers than librarians, but you may well be more likely to meet a librarian than a farmer. If you or I meet someone with all those character traits, I suspect they are more likely librarian than farmer.