Precious (KJV) is used in the sense of "rare." Rare things are usually precious or valuable.
The sense of this is that the priesthood at that time spoke without inspiration; there was "no open vision." Their messages carried no moral authority because God was not with them. Obviously, Eli was not a very good priest, and his sons were even worse. They did not make the truth open or clear to the people; they were not hearing the inspired Word of God. The people were no longer positively affected by the ceremonies being performed by a decadent priesthood, so through Samuel, God raised up a new moral power to correct the situation.
There does not seem to be a systemized process of succession from one prophet to another. Each prophet received his office directly from God by appointment. This is another distinction between a true prophet of God and a priest, even if a priest speaks under the inspiration of God. A prophet was directly appointed by God, whereas a priest received his office simply because he was a descendant of Aaron.
The classic prophet was a man who preached the way of God to the Israelites yet tended to be outside the established system. This becomes clear from Samuel on.
John W. Ritenbaugh
Prophets and Prophecy (Part 1)
Other Forerunner Commentary entries containing 1 Samuel 3:1:
1 Samuel 3:1