If I flip a coin 100 times and get all heads, there are many, many hypotheses that suddenly get a lot more plausible. Perhaps the coin is strongly biased. In fact, a weak prior of slight bias will, post-update, seem much more plausible than the fair coin. Perhaps it's a double headed coin, and in my inspection I failed to notice that. It seems vanishingly unlikely that I would miss that on repeated inspection... but I'm still more inclined to believe that, than a mathematically fair coin coming up heads every time. Perhaps I've unconsciously learned how to predictably flip a coin. Perhaps I've failed horribly at counting, and actually only flipped the coin 10 times. Perhaps any of the above are combined with my not noticing a tails or ten appear in the result string.

In other words, exceedingly unlikely events will make me doubt my sanity before they make me start doubting math.