When thinking about any mathematical topic, visualizing different specific examples of what I'm studying always helps.
For probability theory, I tend to think in terms of possible universes or stock markets when thinking about time series, apart from the more typical coin flips or dice when its applicable.
I think collecting multiple weird and exotic examples can help ones understanding, so that's why I'm asking the question: which exotic/weird/noticable examples do you use for thinking about probability theory (and how does it help you)? (It's ok if the examples are only applicable to very specific domains.)