Take for example the question of where an electron orbits the nucleus. QM says we can't say where, only give a probability.
More accurately QM says there *is* no precise location, only the probabilities. This isn't a matter of the electron being at a particular point, where we lack the ability to determine where it is exactly. In essence the electron *is* a field of probabilities and left to its own devices (e.g. in a remote part of space) is theoretically at every position simultaneously. Only in the presence of other quantum fields does that change - so when an electron interacts with a proton in a hydrogen atom for example, the two sets of probabilities interact with the result that the probabilities associated with the electron are constrained to positions more or less associated with the classical notion of an orbit.
When we attempt to observe an electron's position we necessarily interact with it in a way that constrains its position probability to something close to a single point - this is the only sense in which an electron becomes a "particle". So in the 2-slit experiment, if we don't observe it, the probabilities remain (relatively) unconstrained and there remain possible paths through both slits, whereas if we do observe the electron we narrow the field of probabilities enough to make it almost certain it will only pass through one slit.
(it is therefore meaningless to say "only observe after the particle has passed thru the slit" since there is no "particle" until the observation is made)