How would the military tell the difference between a conventional missile, and a nuclear missile?

for example, if NK launched a nuclear missile at Japan alongside hundreds of non-nuclear missiles, how will JSDF and the US military pick out the nuclear missile to make it the priority target?How would the military tell the difference between a conventional missile, and a nuclear missile?We don't. That's why we also have nuclear missiles for retaliation. MAD has worked for 60 years, no reason it still doesn't.How would the military tell the difference between a conventional missile, and a nuclear missile?It would be completely impossible using any technology i've heard of, to tell the difference between a nuclear and a non-nuclear missile. You'd have to either have incredibly sensitive instruments to tell the difference from a distance, or you'd have to get close to the missile in order to tell if it has uranium or plutonium in it. This is one reason why "missile defence" is a very bad idea now: it cannot tell which missiles have nuclear weapons on board, so it would be very easy for a country to overwhelm any such defence simply by firing a lot of missiles, only some of which are nuclear.How would the military tell the difference between a conventional missile, and a nuclear missile?They have a Magic Eight Ball for that scenario.