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Well it is possible, but not a cheap solution. You could buy a video capture device to capture the output from the PSP3 and then you could use the software that comes with the device to watch the output. Elagato make a number of video capture devices and the eyetv software will let you view the feed. Unless you need the space, you might be better off getting a separate TV.

http://www.elgato.com/elgato/int/mainmenu/products/Video-Capture/product1.en.html

EDIt : Just looked at the detail, does not look like this comes with eyetv, so may not be the best option, but this is the type of thing that you will need.
 
Well it is possible, but not a cheap solution. You could buy a video capture device to capture the output from the PSP3 and then you could use the software that comes with the device to watch the output. Elagato make a number of video capture devices and the eyetv software will let you view the feed. Unless you need the space, you might be better off getting a separate TV.

http://www.elgato.com/elgato/int/mainmenu/products/Video-Capture/product1.en.html

This could result in a poorer quality of video. Possibly frame rate issues.

Go with a new TV.
 
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