Plumbing a Dishwasher

[hadespuppy]

I'm getting a dishwasher delivered in a few days, and there's obviously been one in the space before, but I suspect that the plumbing is incorrect. You can see the hot water at the back, which should be right, but it's the drain that has me concerned. Every diagram I have seen has the drain from the dishwasher going into the sink drain between the sink and the trap, not having a second trap as is the case here.




Is is going to cause any issues if we attach the drain to the second trap, or should we redo the whole thing? The guy who owned this house before us has done all sorts of weird and wonderful things to it, many of them half assed or totally incorrect, so I'm not exactly confident in the existing setup.
I don't have a lot of experience with plumbing, but I don't want to pay for a plumber to come out to do something that I'm sure isn't actually that difficult