You're correct it mostly only works for a spread of predictions that don't have such a large influence on each other.
If one capital gets nuked the odds of another one suffering the same fate skyrocket.
Yeah, it's just about possible to imagine Kyiv or Tehran gets nuked in a "limited engagement" that never escalates further. But if, say, Lisbon gets nuked then the whole world is at war.
Nuclear strikes on N different capital cities aren't statistically independent events, and that kind of computation only makes sense for statistically independent events.