Installing both Call of Duty: Infinite Warfare and Modern Warfare Remastered will get you back at least 130GB of HDD space.
This info comes from the back of the PlayStation 4 version of the Call of Duty: Infinite Warfare Legacy Edition, as revealed by a French retailer.
With the download size for Modern Warfare Remastered being around 40GB, that leaves 90GB for Infinite Warfare, which seems pretty huge. Perhaps that PlayStation Pro support is something else?
If you have pre-ordered the Call of Duty: Infinite Warfare Legacy Edition, don't forget to redeem your code via the PlayStation Network so that you can get early access to the campaign, 30 days ahead of everyone else.