The phrase "fat chance" can be used as a way of sarcastically describing the impossibility of something, but where did it originate from? I've googled it several times, and it always comes up with the definition, not the origin.
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I believe this simply derives from one sense of the word fat:
The term is used ironically. At face value it means there is a large chance of something happening, but underneath it really means there is a slim chance after all.