how probabilities of events feel like

Gut feelings have pretty bad resolution. In particular, I don't think gut feelings can differentiate between, say, 2% and 3%.

As a rough approximation (and, possibly, subject to the typical mind fallacy :-D), I think the gut thinks in these categories, assuming the probability is of something bad happening:

• Too low-probability to even think about it.
• Too low-probability to worry about it unless the consequences are really bad.
• Not likely, but worrisome -- worth guarding against unless prevention is expensive/unpleasant.
• Feels dangerous, there is motivation to do something about it.
• It's coming my way, active measures are called for.
• I'm fucked.

For fine resolution you can train your mind. I'm not sure how trainable your gut is.

Nice idea, but I'm not sure the examples are that illustrative. People who haven't been to Greece have no idea of how common blue eyed people are there, for instance. What you want is something that people have a good grasp of so that they can develop their intuitions. I don't have an alternative suggestions (apart from things like dice throws, but I guess that's not what you want) off the top of my head, though.

I'd advice you to avoid choosing examples, which might have a different perceived probability than the real one in most people - the usual example would be things which often get reported on the news (which leads to them being are perceived as more likely than they are). Alternatively, use those examples but only in conjunction with other [hopefully] less distorted ones.

I'd personally mostly use examples that relate to sports, games and so on - e.g. chance to draw 2 aces in a row from a pack of cards.

I think something that touches closely to what you're trying to do is Rational Poker, which is using poker to train your bias overcoming skill. Specifically the This is what 5% feels like. exercise. The idea is that you can combine your explicitly calculated chance of winning a hand with your gut feeling enough times that they begin matching up. You'll eventually understand what 5%, 10%, 50%, or 90% actually feel like from the inside. Unfortunately, Im uncertain how well this gut feeling generalizes, so using it to determine probabilities outside of areas you've trained it for may be less successful.

Chance of a rolling a double six is ~2.8%, and something that comes up in quite a few games.

Sounds like an xkcd comic. Maybe borrow from his charts?