rarity
Something very uncommon that does not happen or exist often.
A rarity is something that exists in very small numbers or appears only occasionally, making it uncommon and often valuable. A baseball card becomes a rarity when only a few were printed, or when most copies have been damaged or lost over time. A four-leaf clover is a rarity because most clovers have three leaves.
The word means something is scarce enough to be noteworthy. Rain might be rare in a desert, but a blue moon (the second full moon in a calendar month) is a true rarity, occurring only every few years. That's why people say “once in a blue moon” to describe things that almost never happen.
Rarity often increases value. Museums display rarities like ancient coins or fossils because few examples survived. Collectors prize rare stamps or minerals. But rarity can apply to intangible things too: a snowfall in Florida is a rarity, as is finding someone with perfect pitch or a photographic memory.
The opposite of a rarity is something common or abundant. While pigeons crowd city streets by the millions, the California condor is a rarity, with only a few hundred alive today. When something combines quality with scarcity, its rarity makes it especially treasured.