How to turn a cut component video cable into coax?
OTA DTV antenna cable is commonly RG6 (replaced RG59). This is a 75 ohm coaxial cable with an F or BNC termination (probably F). The better quality component video cables use 3 separate RG6 cables with RCA connectors at the end. They are simply attached together in a bundle. My original answer assumed this is what you had.

With the picture you've added it appears you have the more compact 3-way coaxial cable. Each conductor of this cable is 75 ohm and suitable for (composite) video over short runs. Whether it will support the higher bandwidth of OTA Digital is not certain. There's only one way to find out . . .

Solder on a BNC connector F-type coax connectors are crimp or twist on since they don't supply their own inner pin. BNC is fairly common for antenna connectors and has the right bandwidth for the signals you are trying to pass. Only expose as much of the conductor as you need to do a good solder job.

Given that your cable does not have the more common dimensions of an RG6 or RG59 cable it may be difficult to make a mechanically stable connection to a male cable connector. 

I inferred from your question that the antenna cable is already in the living space (not in the wall, per se). Your best option to terminate this cable is a wall plate.

Connect the antenna and component cable directly. If both cables are already in the same wall cavity you can connect them directly (otherwise use a jack as below). Cut off the existing connector on the antenna cable, strip it back a little bit, and connect the inner conductor to one of the component cable conductors and the outer ground sheath to the component cable ground sheath. I would use a small heat shrink tube to insulate the inner conductor and a larger heat shrink tube to cover the ground sheath and give the joint some mechanical strength. 

Install single-BNC wall plate jack(s) You can find these for BNC fairly easily (link). This allows you to make a clean and mechanically stable connection at each termination of the component cable. Or one side only if you directly connected to the antenna cable.

Plug the antenna cable into the wall jack at location B Assuming your antenna cable has an F-type connector use a BNC Male to F Female adapter. These are fairly rigid so probably no need to cut off the connector and replace with a BNC Male connector. You might even find one at a right angle so you cable hugs the wall.

Use a patch cable to connect your TV at location A Use an RG6 patch cable and another BNC Male to F Female adapter.

I should emphasize that I really don't know if a single conductor of your component cable can pass an OTA Digital TV signal. In fact I'm somewhat skeptical. Most OTA Digital stations are UHF so 400 - 800 MHz. NTSC video (single 480i signal) runs at 4.2 MHz. HDTV (single 1080p signal) runs at 25 MHz. We moved from composite video (one conductor) to component video (three conductors) to handle a single 1080p signal. And the connection I proposed above may only support the bandwidth of a composite video cable. Caveat emptor