Previously I've used the design in the image below to prioritize belt flow after a splitter: Unfortunately this will not work perfectly once you need full throughput on your prioritized belt. As shown in the image above some iron ore still pass through the deprioritized belt even though the prioritized belt isn't fully saturated.
Fixing this is fairly simple, so as I still see many use the design above, I thought I'd throw out my solution to the problem: By splitting the prioritized track again then the two new tracks hold 50% of the items that will later be merged, meaning that while the prioritized track is fully saturated the sum of items on the two belts between the two new splitters will never exceed 8 as long as all the items on the prioritized belt are consumed. If all the items on the prioritized belt aren't consumed then the two belts between the splitters will start filling up and the lock on the deprioritized belt will be released.
Note: It's not necessary to send the top output of the rightmost splitter down to the prioritized track, I just dislike loose ends.