None at all

I assume you're referring to the Copenhagen interpretation of quantum theory, which asserts that at the most fundamental level everything comes down to probability. HOWEVER, probability is all it comes down to. This extra "room" in the amount of the world that can be determined can in no way be given to consciousness and free will. Yes, many leading theorists believe at the most fundamental level, the world is based on probability. But that doesn't mean we have a conscious choice as to which probable outcome we take. All it means is that the input we receive and the world around us may have something truly and fundamentally random in it, but our brains still function and react based on these inputs.