Who "owns" a province with besieged fort?

[The Panther]

Movement is simultaneous. Your army moves out and the new army moves it at once, taking the same amount of time to move for either side. You therefore never meet in battle unless you are crossing your armies into each other's provinces. In that case, there is a probablility that your armies will spot each other during movement and fight in one of the two provinces. I have never seen a formula for this probablitity, but it is supposed to be based on the total sizes of the army. This is presumably because larger armies are easier to spot than smaller ones.