Solved! Worked for me at least.
There are 2 methods. I tried the 2nd method first which is lengthy & has low success rates. Did not work for me but might for you. Worth a try.
Try the Method 1 first, if it doesn't work then you may give the second method a try.
I have Synaptics TouchPad driver for a HP laptop. I am not sure about other drivers.
Method 1: Downgrading driver build
-Go to device manager>expand Mice & other pointing devices>right click the Synaptics PS/2 Port Touchpad>Properties> check driver date under Driver tab(mine was 15-7-2015).
-Now click update driver>browse my computer for driver>Let me pick from a list of device drivers on my computer
-Check for Synaptics PS/2 Port Touchpad older dated(mine was 6-7-2015 in dd/mm/yyyy). Click & go next to install the driver. Should ask for restart.
Note: the driver version in the list above will be the same but different dates.
-Restart & go to Synaptics settings & disable Three-finger & Four-finger touch under Tapping tab.
-Click apply, Ok & close everything & confirm that three-finger tap is not working.
-Restart. Ideally that option should not be enabled again. Restart & shut down-start a couple of times to confirm.
If does not work, then you may also try other old dated drivers from the list you found above & follow the rest steps.
Method 2 :
Download HP drivers from HP site & for your model number.
PS: By restart I mean actually hitting the restart button & not shut down-boot again.
Read all the steps at first before starting the steps actually.
-Uninstall the synaptics driver software from program & features. It should then ask to restart.(Again I mean restart & not shut down-start again)
-After restart, delete every folder related to it from Program files or (x86), User>(Name)>App data>Roaming, and any other possible place. Restart again.
-Now install the driver you downloaded, if it's saying you haven't restarted after uninstalling the last time, then restart again & install.
-Go to Synaptics settings & disable Three-finger & Four-finger touch under the Touching tab. Hit apply & ok. Test & confirm if the three-finger tap is not working.
-Close the settings app & all other windows open (which should be none) & restart.
-Make sure you DO NOT open the Synaptics settings again ever. If you do, you might have to repeat the whole procedure all over again from start (experienced).
-Use your laptop a bit for a 2-3mins & confirm the Three-finger tap is not working.
-Restart again & shut down-start again a couple of times to confirm the problem is solved.
I did it around 4-5 times each, restart & shut down-start. It's working all good now.
Edit: a Windows update for Synaptics drivers shows up & installs. Since the installation cannot be stopped in Windows 10, it all goes to square one where you are left with the same problem. Check for Windows updates after the installation of the driver in Method 2, if no updates are shown then this method should work.
Hope either of the methods work for you guys too. Good luck!