If this happened to me I would definitely utilise the company grievance procedure - this type of behaviour cannot be condoned in a work place. You should carefully follow the procedure to ensure that not just you - but others are not subject to an invasion of privacy in the future particularly where other colleagues were present and are not saying anything. An enquiry is your right in these circumstances given that it has already been admitted that they attempted to get in the drawer. A disciplinary issue has definitely been created and at least an enquiry will reveal why a person you do not get on with was the one to actually open the drawer. If you do decide to invoke a grievance system it will be a wake up call to all concerned. I say this without knowing the full facts obviously but hope it helps.
It is a company set of drawers, not a personal locker.....

Been there, done that....
Its the firms locker/drawer/cupboard. If they want in, they will enter, no comebacks from you.....
Trick shown to me by an elder colleague, if you store 'personal' stuff within, is to ensure its also got a good photoshop (or photocopy or falsified carbon copy, depending on your age/technology of the time) of some firms nosey git - generally the office ringpiece that you have to work beside - is in there at the same time in a suitably compromising situation.....
Smokescreen is a recognised military defence, apparently!!