The odds are:
Out of Wilderness: 1 in (350 - combatLevel) where combatLevel is capped to 300.
Inside of Wilderness: 1 in ((350 - combatLevel) / 2) where combatLevel is capped to 300.
So if we have a NPC which has a combat level of 200 and is out of Wilderness, it will have a 1 in 150 chance of giving the supply cache.
If we have a NPC which has a combat level of 100 and is inside of Wilderness, it will have a 1 in 125 chance of giving the supply cache (if it were out of Wilderness, it'd have been 1 in 250).
If a NPC has a combat level of above or equal to 300, it has a chance of 1 in 50 outside of Wilderness, and 1 in 25 inside Wilderness.
The NPC needs to be eligible for the supply cache(there are a few exceptions like Zulrah's snakelings) and the NPC needs to be at least level 50 combat.