3 Monitors in a row and I want the dock in the middle

Switch off 'Displays have separate Spaces' in System Prefs > Mission control.

Then set the middle monitor to be the primary in
System prefs > Displays > Arrangement
by dragging the menu bar to that monitor

After the question edit -
I'm afraid if you want the Dock on the left edge there is no way to achieve this. The above solution only applies if you have the Dock at the bottom, otherwise it has nowhere to 'sit' & will always go to the first 'edge' it can find, which in this case is the left side of the left monitor.

You could try looking at something like DragThing instead, which can be anchored anywhere. I actually anchor mine to the right of my left monitor on a 2-screen setup, which effectively puts it where the red bar is on this image.

Late Edit
DragThing, after 20 years of sterling service, will no longer be supported after Mojave & is no longer available for purchase.

A slight modification of the workaround suggested by bjunix and the accepted answer is to put the right display in the Arrangement of Displays from System Preferences virtually at the bottom, like this

.

Then in System Preferences > Dock > Position on screen = Right will place the dock on the right of the screen which is physically in the middle. You only need to remember that to move to the screen on the right mouse should go to the bottom of the main screen in the middle. It works for me, as I have two external monitors connected to a Mac book pro which is on the right and want the dock on the right of the biggest screen which is in the middle.

I used to work with my Mac Book sitting on my desk, main external scree right behind it and the secondary external on the left in vertical position and was using laptop as a keyboard and the third screen in a layout exactly like shown in the picture (a bit unhealthy). Now with the laptop finally moved to a Kensigton stand with a wireless chargers on the right of the right screen I could not find a way to rearrange the screens in settings and keep the dock on the right of the main screen, so had to go with some "faking". So far, so good, it just gets only a little bit of time to get used to moving to the screen on the right by going "down".

4 years have passed, macOS Catalina 10.15.5 and it is still all the same answer "this is not possible" and "the computer says no".

I cannot believe this is not possible in Mac OS settings and not a property of the system dock and extra software is required to set such a simple thing. With large wide screens in the middle of the multi screen setups the dock at the bottom takes just too much estate and the side of the main middle display is the best place for it. It would be nice for Apple to listen to the users and accommodate this need.

If you want to have your dock on the right or left side, there is an workaround to achieve this by arranging your monitors diagonally. It's not the best solution as you have to move your mouse to the corner of the screen to go to the other space but at least the dock is where you want it.

Credit goes to this answer here: https://apple.stackexchange.com/a/252994/62200