The 3-second rule is only a rule of thumb, and in many cases 3-seconds will not be sufficient distance to the car in front of you. A greater distance is required e.g. when:

The roads are slippery (as in this question)

Driving at high speeds (above 80 km/h)

The car in front is not maintaining a sufficient distance to you

The car behind you is larger/heavier than your own vehicle (as the braking distance will be longer) The car behind you is larger/heavier than your own vehicle (as the braking distance will be longer)