You need four, not three.

You would need three if you had an atomic clock: if you knew the precise time. But in practice you do not. You have a good clock that has an unknown shift with respect to the clocks in the satellites.

So you can measure differences in times, but not absolute times. I.e. you do not know the distance from the gps to the satellites, you know the difference of these distances. So you need a fourth satellite.

This was designed because it is easy to make accurate relative time measurements, but hard to have an absolute time reference.