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.
Just to add to this -- In QM/QFT there is an inverse relationship between energy & distance, meaning small distances (or sizes) correspond to high energy interactions (see e.g. [1]). One consequence is that at small enough scale (the Planck scale), the energy scale gets so large that quantum gravity effects are expected to be non-negligible. Formulating a theory of quantum gravity that fits into the Standard Model of particle physics & agrees with general relativity is an open problem in physics, therefore the Planck scale is at least the smallest distance that can conceivably be modeled given our current knowledge.
An electron moves as a wave that satisfies Schrödinger's equation. Maybe that wave goes through a Young's double slit then hits a wall of detectors. We get a detection. But, the electron was never a point particle that hit the detector. Instead the wave of the electron hit one of the waves in the detector -- no points were involved.
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.