(Continuing the 'real-world' application of this)
Assuming Eve only wants to steal 'useful' items, or assuming you can generate an infinite number of padlocks (which you can on a computer), you could just let Bob send Alice his unlocked padlock, then Alice locks the medicine in the chest. Of course, this has the slight problem, where Alice could swap the padlock for one of her own.
In the real world, that basically means, you can give everyone a copy of your RSA public key (padlock), because it's only useful for encrypting (locking) things, you need the private key (the key) to decrypt (unlock) it -- however you need to be sure you have the correct padlock, lest you be tricked into encrypting something to some evil third party.