Sony has an option that allows users to turn off HDCP during gameplay.
First, connect your PlayStation 4 directly to your TV set or display via HDMI, without using Elgato Game Capture HD60 Pro.
Visit the Settings > System section of the PlayStation 4 interface, and turn off Enable HDCP.
After that, you can use your PlayStation 4 with Elgato Game Capture HD60 Pro.
Install Elgato Game Capture HD60 Pro inside your computer, and reboot.
Connect your PlayStation 4 to the HDMI In of Elgato Game Capture HD60 Pro via an HDMI cable
Connect the HDMI Out of Elgato Game Capture HD60 Pro to your TV or display via an HDMI cable.
PlayStation 4 (PS4): General HDMI output
Content other than gameplay may still be encrypted with HDCP (High-bandwidth Digital Content Protection). In that case, Elgato Game Capture HD60 Pro will not be able to capture that content via HDMI.
The PlayStation 4 uses HDCP protection when watching a purchased movie, or using services like Netflix or Hulu. Therefore, Elgato Game Capture HD60 Pro won't be able to capture that content.
Instead, you will get an error message that states:
Cannot start the application.
You must turn on [Settings] > [System] > [Enable HDCP]