In Bead Jar Guesses, I made a slightly clumsy attempt at carving out a kind of guess based on so little information that even a rationally-supposed, very small probability of some outcome doesn't confer a commensurate level of surprise when that outcome occurs. Here are several categories of probability assignment (including a re-statement of the bead jar thing) that I think might be worth considering separately. (I'm open to changing their names if other people have better ideas.)
Bewilderment: You don't even have enough information to understand the question. What is your probability that any given shren is a darkling? What is your probability that Safaitic is sometimes recorded in boustrophedon? What is your probability that 你有鼻子? (Ignore question 1 if you have read Elcenia, especially if you've seen more than is currently published; ignore question 2 if you know what either of those funny words mean; ignore question 3 if you can read Chinese.) In this case, you might find yourself in a situation where you have to make a guess, but even if you were then told the answer it wouldn't tell you much in the absence of further context.1 You would have no reason to be surprised by such an answer, no matter what probability you'd assigned.
Bead Jar: You understand the question, but have no information about anything that causally interacts with the answer. To guess, you have to grasp at the flimsiest of straws in the wording of the question and the motivations of the asker, or much broader beliefs about the general kind of question. What is your probability that Omega will pull out a red bead? What's your probability that I'm making the peace sign as I type this question with the other hand? What's your probability that the fruit on the tree in my best friend's backyard is delicious? Like Bewilderment questions, Bead Jar guesses come with no significant chance of surprise. Even if you have a tiny probability that the bead is lilac, it should not surprise you.
Bingo: You understand the question and you know something about what causes the answer, but the mechanism by which those conditions come about is known to be random (in a practical epistemic sense, not necessarily in the sense of being physically undetermined). You can have an excellent, well-calibrated probability. Here, there are two variants: one where the outcomes have mostly commensurate likelihood (the probability that you'll draw any given card from a deck) or one where the outcomes have a variety of probabilities (like the probability that you draw a card with a skull, or one with a star). You shouldn't be surprised no matter what happens in the first case (unless the outcome is somehow special to you - be surprised if a personal friend of yours wins the lottery!), but in the second case, surprise might be warranted if something especially unlikely happens.
1About 5/6 of shrens are darklings, depending on population fluctuations; Safaitic is indeed sometimes recorded in boustrophedon; and 有 (I hope).