[Slippery Slope]

I used the empty box method, now they are opening an investigation with the courier.
What should I expect?

If you play your cards right, you can get out of this easily. It's all about execution.
You could expect to have proof of filing a police report. I've been asked before, questions like - "Have you reported this to the police?" - I always talk to them directly over the phone, which I find to be the best method if you're good with confrontation and quick with witty responses. Simply tell them, "Yeah, I've called the police and they're looking into this aswell."
Don't sound stern, just have a chill conversation with the agent. Use their names when you're talking to them and be respectful.

They'll of course offer you a refund or a replacement item.

You: "Yeah, Tom - when the box arrived, the products original packaging was in there, but it empty. It's clear now that I look at it closer that the original tape has been 'taped over' - this is ridiculous."
He'll say something like. "Ah, I'm very sorry to hear that, *name* - Let me see what I can do for you."
Proceed to receiving your refund.

EDIT: I just re-read the thread. Most of the time, it's the same case as you doing the receiving of the empty box method. You should be okay.