This checks which player is searching a library, not which library is being searched.

The search works exactly the same as normal except that the player doing the searching sees only the top four cards of that library. The player can’t look at the other cards in that library at all. Cards not in the top four cards of the library can’t be found in the search, even if they’re identifiable in some manner.

After the search is complete, if the effect has the player shuffle that library, the entire library is shuffled.

If the player is searching the top four cards of his or her library, the player may cast a Panglacial Wurm located there.

Shadow of Doubt prevents libraries from being searched at all, so its effect trumps this one.