In Godfather II, what happened that led Michael to know his brother had betrayed him?

"Fredo betrays Michael when approached by Johnny Ola, an agent of rival gangster Hyman Roth during the negotiation of a business deal between Roth's organization and the Corleone family. With Ola and Roth claiming that Michael is being particularly difficult in the negotiations, Fredo secretly agrees to aid Ola and Roth in exchange for compensation. The film never reveals what specific assistance Fredo provided Ola and Roth against Michael, but this betrayal ultimately results in an assassination attempt against Michael at his Lake Tahoe home. Fredo later ambiguously claims that his goal in the secret deal had been simply to enrich himself in a manner that did not require him to be dependent on Michael to "take care" of him, but swears that he did not realize he was being used as part of a larger plot to kill his brother. This seems to be supported by a scene where Ola calls Fredo in the middle of the night, and Fredo says that he wants nothing to do with him, and that he was lied to."

"Michael discovers Fredo's role in the plot during his trip to Havana when Fredo, forgetting that he had previously told Michael that he'd never met Johnny Ola, lets it slip out that he and Ola had been in Havana together. Michael confronts Fredo later and tells his older brother, "You broke my heart." In the ensuing fray, Michael pleas with Fredo to come with him, since he believes Roth is dead and Fredo is still his brother, but Fredo, remembering that Michael used this tactic to kill Carlo Rizzi, instead runs away. He is eventually tracked down and convinced to return home."

Yeah, it was the part where when they were sitting to have dinner, Fredo denies knowing him, and then when they were all in that room together watching some freak show, Fredo lets it slip out to another guy that he and Johnny have been there before.
I love the Godfather trilogy.

Couchcarrot, sabrewolfe:

Thank you both for your excellent answers to my question.