It'd be one thing if those probes remained in near-space. There are of course advantages to a country having its own exclusive information strategically and possibly for future space-mining.

Deep space is quite literally as far away from that as it gets. There's no realistic mission that far out in our lifetime or the lifetimes of our great grand children that will have any realistic return for a nation beyond pure exploratory interest.

If Russia or China are really interested in objects far outside our solar system, they're probably better off sitting back and letting NASA do it, given that they don't have to wait decades to do so. Something tells me that neither of them actually cares, though.