Not as I understand it. I think of it as: A and B were correlated, and now you caused B and C to become correlated. That cannot possibly imply that A and C's correlation dropped to zero.

Or if you prefer to think of balls; if A hits B, and then B hits C, then C's future trajectory is still (forever) affected by what A was doing, as is the trajectory of anything else it hits.

That is classical systems and "classical" probability. In quantum systems particle functions collapses all the time making parts of it go to zero. At least as we understand quantum mechanics today, the math we have doesn't explain experimental results without those collapses.

Yes of course I know that's classical, I was just making an analogy to get the point across about correlations.