Fat chance

Why "fat chances" means low chances? "Fat" implies a big amount of something not at all something small.

In my language (romanian) we say "slim chances" for low chances!

"Fat chance" (no "s") means very little chance. The speaker is being sarcastic.

In my part of the U.S., I have heard: "The chances of that happening are slim and none" and "Chances are slim that it will happen." But I have never heard "slim chances."