How to connect a finger probe sensor (SPO2 sensor)to an arduino board?

You need to find out how the sensor works.

These sort of devices were fashionable in laptop computers 6 years ago, they don't seem to be
so common now. There is quite a bit of processing involved in matching fingerprints. This
could be done inside the sensor, or more likely, the software to do it, is on the computer.

You need to search around, and see what you can find about the process, it may be difficult
as the makes of these gadgets would not be disseminating that information widely.