Since you have chosen to present the problem in abstracto, I am assuming that you are not so much worried about the exact nature of determining.
The first, most simple formalisation that comes to mind is:
s(x) ... the state of x.
D(x) ... x determines what c does.
Then we would write
◊a = s(b) ... possibly a is the state of b
D(s(b)) ... the state of b determines what c does.
◊D(a) ... possibly a determines what c does.
So does the last sentence follow from the first two? No it does not, one has to replace the second sentence by
□D(s(b)) ... it is known that the state of b determines what c does.
Now the third one will follow, at least in, say, S4 which was the epistemic system that Hintikka settled for. If am not mistaken, the reasoning should go through in K already.