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For in battle, the rate is based on how many HP the enemy has left. It's 1- (% of total HP -5%). For instance if the enemy has 12% of their health left, there's a 93% chance to steal.
You can also increase this with boosting, not quite sure of the formula though.
For NPCs, it's pretty simple. The higher Throne's level, the higher the percentage.
https://www.reddit.com/r/octopathtraveler/comments/11ee9o1/path_action_skill_ups_thieving_tips_tricks_etc/
Also, if its an item you really want it might be worth checking other characters for Purchase/Entreat/Mug. Some items/NPCs are much easier with a different action.