What happened to him is so incredible that he cannot even explain it. It would sound a cock-and-bull story

Il sospetto ladro pensava che la polizia avrebbe creduto alla sua storia piuttosto inverosimile, e cioè che aveva trovato tutti quei soldi in un cestino nel parco

The suspected burglar thought the police would believe his cock-and-bull story, which was that he had found all that money in a trash bin in the park

Dove sei stato tutta notte? E non raccontarmi la balla che hai finito la benzina e poi sei finito, a piedi, a casa del diavolo cercando un distributore

Where have you been all night? And don't give me some cock-and-bull story that you ran out of gas and got lost in the middle of nowhere looking for a gas station