Strands of Arcane Power

[Olive]

And if a province has already been searched by this spell at, let's say, level 1. Is there a chance that it may be searched later at a higher level ?

[Soyweiser]

yes

[militarist]

The more interesting question is if Strands has limited searches per turn, or each province in dominion has equal possibility to be checked, and this probability doesn't depend on amount of provinces and distance from capital.