1, PS4

PS4 has disabled HDCP for firmware 1.7  or later, so use can easily record game play with ezcap game capture solutions.  
Please update firmware of your PS to 1.7 or later. And go settings---System disable “Enable  HDCP” option. Then connect PS4 to  ezcap HD video capture with HDMI cable, you will see the game play picture  pass throught on monitor, and you can record video now. 

2, PS3 

- Why can't record video  through HDMI port of PS3?
It's maybe because of  HDCP protection of HDMI signal, please buy one HDMI splitter to decode HDCP, or  record video through the component video output. Please note, decoding HDCP is illegal in some countries and areas.  

- Works with PS3 through  Component connection:

Because the HDMI  out of PS3 has HDCP protection, so there is no way to connect it directly to  ezcap game recorder with HDMI cable, so the first suggestion is to use component cable  connection. Go to the settings---Video  output settings, choose “Component/D-Terminal”. At the resolutions setting, make sure  the “1080P” option is NOT be ticked, otherwise some game play (e.g. GT5) cannot  be recorded. 

- Works with PS3  through HDMI connection:

If don’t have  a component cable, and want to record with HDMI output, then you need a device  such as a HDMI Splitter which can decode HDCP protection, and you can record video when you get pass through on monitor. 

- Why can't record audio from PS3 by HDMI port?  
Please go to PS3 settings --- Audio output  settings --- select HDMI and choose Manually. Don't tick Dolby and DTS,  then save the setting.