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Catelyn and Rodrik arrive at King's Landing by boat (before Eddard and Robert) and try to be secretive about their investigation into the assassin's fancy dagger. But Petyr and Varys find Catelyn and promise to help her.
(Apparently Petyr was fostered with Catelyn and her sister at the Tully castle Riverrun; but Petyr fell in love with Catelyn, which was kind of a social no-no. Still, he appears to be friendly. Maybe too friendly.)
Petyr examines the dagger and tells Catelyn that it's Tyrion's: Tyrion won it off of Petyr at the last tournament, when Tyrion bet against Jaime Lannister in a jousting contest.