I answered their questions 'to the best of my knowledge'. [=I gave the best answers I could based on what I knew, but I might have answered differently if I had known something else]
No one arrived late 'to my knowledge'. [=I am not aware that anyone arrived late, but it is possible that someone arrived late and I don't know about it]
They went on vacation, 'safe in the knowledge' that the farm would be well cared for while they were away.
(..) Potter? They will be punished in a manner consistent with the severity of their transcription, further more... Any person found to have knowledge of these events... who fails to come forward... ... will be treated as equally guilty. Another... If anyone in here has any knowledge of (..)2011 Harry Potter and the Deathly Hallows: Part 2