understand is that the domain in which the wave function is sensibly different from zero corresponds to the spatial region within which the atom in question has a chance of being detected. So, if the hydrogen atom, at time $t= 0$, was localized in a sphere whose radius is approximately equal to the Bohr radius, i.e., $r_0 = 5.3 \times 10^{-11}$ m (that is, its probability of presence in that sphere, at time $t=0$ s, is equal to $1$), what we have determined is that after for example $1$ s, that localization radius will have approximately grown to about $50~{\rm km} = 5 \times 10^4$ m.

What we are interested in is to estimate the probability with which we can detect the atom not in any location of this macro-sphere of $50$ km of radius, but in a predetermined sub-region of it. Indeed, if we later want to extrapolate our reasoning to an entire macroscopic structure, it is necessary that every atom forming the structure will re-locate in a very specific place in relation to all the other atoms of the structure, so as to reconstitute it in every detail. So, let us suppose that this sub-region corresponds to a 