I know that this is a common error in argumentation that people make, but I don't know if there is a term for it. It's when people argue from an event being remarkable because of its low probability, without considering the probability of having observed any event that's similar enough to the one they just observed to elicit the same reaction. Is there a name for this fallacy?
For example, a player plays a game in which they have three rolls of a six-sided die. They roll a "4" on a d6 for all three rolls. They remark, "wow! The chance of that happening is rare, therefore the probablitity must be the rare probability 1/216. As a deduction:
P1: I have rolled (4,4,4).
P2: Based on my emirical experience, this is rare!
C: Therefore, (4,4,4) occuring in 6^3 events indicates the rare probability 1/216.
In fact, they would have had a similar reaction if any of the digits 1-6 was rolled 3 times in a row, for which the chance is 1 in 36, not 1 in 216. In the extended circumstance, they may even wager on such a persuasive, but falliable reasoning in a game of chance.
The general fallacy is as follows: Suppose there's some class of events, E, of which the specific event e is a member, and all of which would elicit the same response from an observer. The probability of observing any event in E is p, while the probability of specifically observing event e, is q < p. An observer observes event e, and considers it a remarkable coincidence because of the low value of q, when in fact, they should be considering the value of p. Lastly they use a intuitionally fuzzy measure 'rare' which conflates q and p in drawing a conclusion.