Treasure chests are determined by a number of things:

Chance of appearing on the map
Chance of containing Gil (amount of Gil is a random number in a range of numbers, say 200-500)
Chance of containing 1st Item (common)*
Chance of containing 2nd Item (rare)*
Whether or not they respawn

*The 1st and 2nd Item of a treasure chest changes when equipped with Diamond Armlet.

The Henne Mines treasure chest with the Zodiac Spear has the following:

10%
90%
90%
10%
No

To get the Zodiac Spear, the probability is (0.1) x (0.1) x (0.1)

(Probability of Chest appearing) x (Probability that the chest will contain an item and not Gil) x (Probability that the item is the 2nd item, the ZS)