First, and mostly irrelevant, is a definition thing: a fossil resource comes from organic decay. Oil and coal mostly come from ancient prehistoric forests. As far as we know, you can't find these outside earth and even the most optimistic projections do not expect oil to last more than one more century (pessimistic projections are surprised it did not stop yesterday. Without shale oil we would be past peak oil.)
It has an important consequence: coal and oil can only be found on a relatively thin layer of the earth, its outer crust. Uranium on the other hand can be found outside the earth (we have found some of the moon for instance and it is a mineral: all planets are expected to have some) and inside the mantle. Actually, the deeper we go, the more we expect to find. It is believed that the heat of earth's center is partly caused by fission reactions.
Second, it is not scarce like oil is. Known reserves may seem small but mineral resources tend to plateau at ~80 years of global consumption as it is usually not profitable to do exploration at a higher pace than that, so the actual reserves are probably much more and likely very extensible as we improve our boring techniques. It is pretty realistic to say we have several centuries of regular uranium for the most common fissile reaction used in power plants.
Third, we have mastered more than one nuclear reaction for energy production. And by that, I mean that we have demonstrated their use on industrial scale: we know how to use plutonium and uranium-238, an isotope of uranium that is 100 times more common than the one we use in regular power plants. Huge plants using these have been built and operated. They are a bit more complicated and expensive, but they work.
With these known and industrialized tech, and only accounting currently known and profitable reserve, you reach an amount of reserve that has to be counted in tens of millennia. And that is not counting reactions that we know work from experimental reactors, or more futuristic prospects like nuclear fusion.