How can I capture/convert HDMI from an HDCP protected input?
You would need a device that supports HDCP if your output source is utilizing it.  That's the entire point of the system.  The video signal is encrypted and will only exchange the data with a device which can cryptographically authenticate itself as an authorized HDCP receiver. Getting that certificate requires proving that they are going to follow the rules on what can and can't be done with the content (such as not allowing it to be recorded.)

Occasionally codes are cracked, but these codes are then removed from the valid list of codes in future products and they won't work on newer material until another code is broken.  It is also worth pointing out that (unfortunately), if you live in the US at least, such bypassing is illegal in the United States according to the DMCA which specifically prevents bypassing protective measures even if the use would be fair use.

It looks like it may also be possible to connect the PS3 to a non-HDCP device, which would prevent it from using HDCP.  If that is the case, then if you could find a device that isn't HDCP compatible or that can strip the HDCP information, then you could get an unprotected stream and do an end run around DMCA limitations.  You may have to do a soft-reset of the PS3 to get it to recognize a non-HDCP TV if it was previously attached to an HDCP one however since it starts up in the same mode it was in for the previous display.