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Related to Buckley's chance: Buckley's and none
Little to no chance of something. Of uncertain origin, it is either a reference to "Buckley's and none" (a pun from the former department store Buckley's & Nunn), or to the escapades of the escaped colonial convict William Buckley. Primarily heard in Australia. I'd say you have Buckley's chance of getting that loan approved.
See also: chance