Because your laptop has an HDMI port and your Playstation 3 outputs its display via HDMI, you might think you can use your laptop as a makeshift screen to play your PS3 games. Unfortunately, unless you have a laptop that specifically accepts HDMI input, this isn't possible. HDMI-in is a rare feature for laptops, so it's unlikely that you'll be able to connect your PS3 to your PC to play games. There are some possible workarounds, but they have substantial issues, so you probably need an alternative approach.
Is Your Laptop Compatible?
The most important concern when you want to play PS3 games on a laptop screen using HDMI is whether your laptop has an HDMI-in port. Most laptops only have one input that is specifically intended to output a signal rather than receiving one as an input. In some rare cases, your laptop may have an HDMI in port, and it is labeled "HDMI In" in that case.
However, this is rare, to the point where you have to specifically look for a laptop with the feature to realistically find it. If your laptop has the feature, you can easily achieve your goal; if not, you likely won't be able to.
If It Isn’t Compatible
If your laptop doesn't have an HDMI-in port, you need to work out the best approach to achieve what you hope to do. You could possibly use a capture card, but these are expensive, and they present problems, so it's likely better to find an alternative solution. You may find that buying a second-hand TV screen or monitor with an HDMI port is cheaper and more effective than finding a workaround for your laptop.
An alternative for PS3 games is to obtain the games through Steam, Epic Games or direct downloads. Many laptops can run PS3-era games. Making this new purchase will probably be cheaper than finding another workaround.
The Problem With Capture Cards
It is possible to display gameplay on your PC via HDMI using a capture card, but there is a significant problem with this approach. The capture card introduces latency when you use the PC as your primary display. A several-second delay makes gameplay impossible on all but the most relaxed and low-tempo games.
PS3 Play on a Laptop Monitor
If you're lucky enough to have a laptop with an HDMI input port – and only in this case – can you get your PS3 to play on a laptop monitor. If this is the case, you can do so easily. Connect one end of an HDMI cable to your PS3 and the other end to the HDMI-in port on the laptop. Switch on the PS3 and ensure your laptop is switched on. The screen changes to the PS3 input, and you can play your games as usual.