Doch does actually not mean "surely" in this context. It strengthens the emphasis on the "sicher" here which is something different.
Du kennst sicher den Rudi?
Would mean very much the same thing without the doch -
You surely know Rudi?
Doch is a particle that can be added to interrogative sentences to express (1) a hope for confirmation or express (2) you mean to know the answer, but it escapes you for the moment.
(1) Du kennst doch bestimmt Rudi?
Definitely asks for a "yes" as an answer, implies you expect he knows Rudi. Note the doch can go with adverbs other than sicher.
(2) Wie heißt dein Freund aus München doch gleich?
Expresses "I'm meant to know it, but can't come up with that name for the moment."
Doch and sicher are not a pair here - doch can be used with other words in questions as well, see my examples.
In non-interrogative sentences, the particle doch can have slightly different meanings, typically putting emphasis on a statement - but you should be able to look that up in a good dictionary.