I have been digging causality recently, and I cannot understand what the "do-operator" does. Like I understand how it relates to the notion of intervention, like "what happens to our system when this happens", but I don't understand the difference with a simple "conditioned on/knowing" operator. 

I feel like the semantic difference is that the "knowing" operator always relies on the probability that X happens, whereas do(X) is more deterministic.

Is my intuition right or somehow right? Or did I get something wrong?