How likely are we to get into a war with a "stable state"?
It was highly likely in the leadup to WWI and WWII, moderately likely during the Cold War, but now is very unlikely. Nearly all military conflicts between two countries in living memory have been asymmetric wars - the relative military power of both countries isn't even close. Often, it's not even countries who are at war, but a country at war with a paramilitary or terrorist organization or a country experiencing civil war.
But to go back to your question, it's very unlikely, as this graph shows. And that's great because we're at the point that a conflict between two major powers would be a world-destabilizing event.
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