The symptoms appear to have no possible connection to each other.

"Do you know what possible connection there might be between the two incidents?"

After this, a massive network of possible connections suddenly became available.

It was a relief to have to go back to teaching class the next two days, but he did find one possible connection.

That lets him out of any possible connection with it.

"How far down the road does one have to go to reveal all possible financial connections?"

What possible connection could we have with such a matter?

All of these people have a possible connection to the poet.

But they had not definitely ruled out a possible connection.

Then they only just learned of your possible connection to the subject?