What is the formula for pickpocketing chance in Fallout 3?

In Fallout 3, the chance of successfully pickpocketing an NPC is determined by a combination of your Agility, the Pickpocket skill, and the target's Perception and Luck. The base chance starts at 20% and is modified by your Pickpocket skill level, with higher skill levels increasing the percentage. Additionally, certain perks and the target's awareness may also influence the success rate. Overall, stealth and strategic planning can enhance your pickpocketing success in the game.