For training the left hand fingers to hover over the fingerboard, it is useful to imagine each of the fingers is a member of a team of helicopters practicing touching down and lifting off. The game is to try to have each finger touching down and lifting off at the exact same speed and hovering at the same elevation off the landing pad (the fingerboard) when not touching down.
Play an A major scale on one string with the finger not playing the note hovering at the same distance as all the other. Practice moving the fingers at the exact same speed (try different speeds) and hovering at the same elevation (try different elevations) over the string.
It is easier to play rhythmically if the fingers don’t each have to travel a different distance to reach the string. Once a finger has left the string, the fingertip has no effect on the string. In general there’s not much point in raising the finger very far off the fingerboard. Note, this game isn’t successful if the left hand is being used to hold up the violin. Great posture and a comfortable set up are required for success.