(that's a) likely story spoken informal
Used to tell someone when you doubt or do not trust something that they said.
She can't be your new girlfriend. That's a likely story!
You may think it's a likely story but I nearly got into an accident just 10 minutes ago.
A: "I just ate the whole cake by myself." B: "That's a likely story."
Used to implicate utter incredulity in something said or believed by someone else.
An exclamation given to express the feeling of disbelief in something that has occured
Used to demonstrate things which never or unlikely happen.
To suspect that someone is being dishonest
Said when you do not trust what someone has promised
The phrase has appeared since at least the 1600s but in a literal meaning to describe a story that is credible. Perhaps until the early 1800s, it began to be used ironically to express the opposite meaning.
To say the same thing repeatedly
Ok, I get it! You sound like a broken record, seriously!