The court heard Cowen was pulled away from Mr Carey by others in the room and restrained on the ground before police were called.
The victim was treated in hospital for a stab wound to his left bicep.
When Cowen was arrested he was searched and found to have another kitchen knife in his pocket, the prosecution said.
Mrs Scott Bell said Mr Carey had been a member of the Countdown fan club since 2011 and knew Cowen from other events.
Cowen, from Morecambe in Lancashire, was not present in court as jurors were told he is “seriously mental unwell” and in hospital.
He appeared on Countdown in 2017 and scored the third-highest total score during his series.
He competed in a further 11 episodes, winning eight consecutive contests, before being finally defeated.
Cowen’s sentencing hearing was adjourned to 30 September pending psychiatric reports.