How can I use this HP power supply as hobby power supplly
It may be one of those "smart" power supplies that is expecting communication with the laptop it is intended to power.  It powers up the laptop, but if nothing is heard within a few seconds, it shuts down.  The third wire is the communication channel.

If this is really what is going on, then no, you won't be easily able to use it for hobby projects.

If it's a popular model, someone may have reverse engineered the protocol or somehow obtained the specs and published them on the web.  Look around and you might find directions on how to hack the supply.