Albus watches the written conversation, and watches Severus eat, seemingly deep in thought before he picks up a pen himself. "I have no wish to return to a world of paranoia...while proof may be difficult to come by, I would at least prefer probable cause. At the moment, I have none. Has something come to light for you?"
He also throws a thought at Severus directly. If there is anything you don't want to directly say to our host, that can remain spoken this way.