you have two bits of information. One is if you hover the mouse over the supply indicator on your stack you'll see supply used per turn/supply stock in the stack (ie organic 2 turn supply + wagons). Keep an eye on this, if its stable, then the province is safe, it its dipping you need to find a way to pull in supply.
If you don't own the province, you can't take any (or not much) local supply, so you need wagons and an active supply line. If you own it you'll see on the province tool tip that it produces x supply per turn. So compare this to the demands of your forces and see how you stand.
Finally use the supply map mode. That will help you to see both where your supply is produced and where it is pushed to. Ideally unless you are on an active campaign, you don't want a large army hanging around in a province that is not connected to your core supply system.
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