There are no hard circumstances under which to pick a lock. You stand there and click with a hoe.
As to Riskae's point, I agree. A 4-digit lock combination lock would be perfect. It's still vulnerable, as combinations can be guessed and you can share with trusted players.
They would cost a certain amount, but not so much that you could only have one double chest of valuables only. That's another main problem with having to pay for locks - if it cost too much, you'd only be able to lock a few chests at most. And I really don't know who would want to pay for a lock that lockpicks are readily available for.