But at least until World War 3, the Nuclear Non-Proliferation treaty and the general trend of less nuclear weapons and developing countries not having the technology would have held in place. Other countries don't have nuclear weapons because of technology, they don't have them because they didn't want to build them and furthermore weren't allowed to. South Africa had nuclear weapons, but they disarmed them and ended their nuclear program due to international pressure. So until World War 3 actually started and the structure of international law fragmented, no nation could have a nuclear program without the treatment that Iran and North Korea are currently subject to, namely massive, economy-crushing sanctions. Regardless of whether or not you have the technology (which would still be a highly guarded secret and would take a few years to work out, as Iran and North Korea have been doing for a decade), it takes a while to refine the uranium required and actually put it into practice as a warhead. There is no way a country like Ethiopia could have nuclear weapons this soon after the war, even if they went straight into developing them the second the war started. In a few years, sure.