With quantum mechanics it's just infinity in the opposite direction, going infinitely small. My very pedestrian understanding is that the field of quantum mechanics came about because people were having trouble explaining the behavior of atomic particles, particularly electrons, using newtonian mechanics, and quantum mechanics were able to explain everything in a more comprehensive framework. At first I always found the idea that electrons are 'nowhere' until they are observed very mysterious, but it made a lot more sense when I understood that probability densities are involved in qm equations. There's usually a similar source of confusion when we move from "probabilities" of discrete distrubutions, which is quite easy to understand, to probability densities, which can be done by taking limit of number of possible states to infinity, and where you can get "probabilities" larger than one.