In the chapter 5 of the Probability Theory: Logic of Science you can read about so-called device of imaginary results which seems to go back to the book of I J Good named Probability and the Weighing of Evidence.
The idea is simple and fascinating:
1) You want to estimate your probability of something, and you know that this probability is very, very far from 0.5. For the sake of simplicity, let's assume that it's some hypothesis A and P(A|X) << 0.5
2) You imagine the situation where the A and some well-posed alternative ~A are the only possibilities.
(For example, A = "Mr Smith has extrasensory perception and can guess the number you've written down" and ~A = "Mr Smith can guess your number purely by luck". Maybe Omega told you that the room where the experiment is located makes it's impossible for Smith to secretly look at your paper, and you are totally safe from every other form of deception.)
3) You imagine the evidence which would convince you otherwise: P(E|A,X) ~ 1 and P(E|~A,X) is small (you should select E and ~A that way that it's possible to evaluate P(E|~A,X) )
4) After a while, you feel that you are truly in doubt about A: P(A|E1,E2,..., X) ~ 0.5
5) And now you can backtrack everything back to your prior P(A|X) since you know every P(E|A) and P(E|~A).
After this explanation with the example about Mr Smith's telepathic powers, Jaynes gives reader the following exercise:
Exercise 5.1. By applying the device of imaginary results, find your own strength of
belief in any three of the following propositions: (1) Julius Caesar is a real historical
person (i.e. not a myth invented by later writers); (2) Achilles is a real historical person;
(3) the Earth is more than a million years old; (4) dinosaurs did not die out; they are
still living in remote places; (5) owls can see in total darkness; (6) the configuration of
the planets influences our destiny; (7) automobile seat belts do more harm than good;
(8) high interest rates combat inflation; (9) high interest rates cause inflation.
I have trouble tackling the first two propositions and would be glad to hear your thoughts about another seven. Anybody care to help me?
(I decided not to share details of my attempt to solve this exercise unless asked. I don't think that my perspective is so valuable and anchoring would be bad.)
UPD: here is my attempt to solve the Julius Caesar problem.
A couple points.
Jaynes would emphasize background information I that provides the contextual information that allows a meaningful estimate. Without identifying and specifying that contextual information as something specific, the mind spins round and round on hypotheticals, and you will "notice that you are confused".
I've found it helpful to specify that background knowledge, even if I'm not committed to it. Then do the math for alternatives scenarios as well. You can't estimate until you narrow down reality enough to have some meaningful scenario where you can make causal inferences.
Another point Jaynes makes. You have to be very clear on what the facts are. Many "facts" are reports about facts by others, continuing a chains of artifacts, reports, and communications. Is the evidence the book you see in front of you, or the assumption that the reported historical and translational lineage of the the book in front of you is accurate back to the original author?
For example, you say
P(no crypt|no Julius Caesar, All known reports on Caesar) is a very different animal than P(no crypt|no Julius Caesar, No known reports of a Julius Caesar exist). If you have a zillion reports on Caesar, and he didn't exist, it would seem that someone did a good job pretending that he did exist. Wouldn't they want make a pretend crypt too? Maybe not, but on balance, probably. This can be more causally circumscribed by I = All reported contemporaneous reports occurred.