"Is the fetus growing in [pregnant woman you both know]'s uterus a boy or a girl." There is a tremendous amount of people who think that order of birth, shape of belly, pulse on pinky, etc can be used to predict the baby's sex [anecdotally these results, combined with peoples' guesses come to 50/50, go figure!] , which if enough of them agreed could arguably be used to marginally move away from the base of 51/49. This probability could be updated after an ultrasound, but still not move to 100% as there are well documented error rates associated with sexing a baby via ultrasound. Even more fun, these error rates are result specific, (i can't remember the numbers, they are buried in a baby book) a "boy" result is wrong less often than a "girl" result, and I seem to remember there is user error involved (some technicians are wrong less often than others). If a blood test is done on a fetus it could be used to further update the probability. The final test, inspection upon birth, which will update the probability again, will not quite get to 100% unless tests were done to rule out a rare abnormality (ie apparently a boy, but has an ovary)
When I explain to people how beliefs should be expressed in probabilities, I would like to use an example like "Consider X. Lots of intelligent people believe X, but lots of equally intelligent people believe not-X. It would be ridiculous to say you are 100% sure either way, so even if you have a strong opinion about X, you should express your belief as a probability."
Trouble is, I'm having a hard time thinking of an example to plug into X. For an example to work, it would need the following properties:
Factual question. So no value-laden questions like "Is abortion morally acceptable?" or counterfactual questions like "Would the US have won a war with the Soviet Union in 1960?"
Popular and important question. The average person should be aware it's an issue and care about the answer. So no "My aunt's middle name is Gladys" or "P = NP."
High uncertainty. Reasonable people should be reluctant to give a probability >90% or <10%
No opportunity to gain status by signaling overwhelming support for one side. So cryonics is out, because it's too easy to say "That's stupid, I'm 100% sure cryonics won't work and no intelligent person could believe it." I'm assuming in any debate where you can gain free status by assigning crazy high probabilities to the "responsible" position, people will do just that - so no psi effects, Kennedy assassination, or anything in that cluster. I need a question with no well-accepted "responsible" position.
Minimal mindkilling effect. My previous go-to example has been global warming, but I keep encountering people who say that global warming 100% for sure exists and the only people who could possibly doubt it are oil company shills. Or if I were to try the existence of God, I predict half the population would say it's 100% certain God exists, and the other half would say the opposite.
So what are the important questions that average (or somewhat-above-average) people will likely agree are complicated open questions where both sides have good points? And if there aren't many such questions, what does that say about us?