My MacBook Pro shut down unexpectedly and now when I try to restart it beeps 3 times while the on-light flashes then goes black again.

Three beeps correlates with RAM memory problems. If your MacBook is an older one, it may have RAM DIMMs in sockets, and those can be upgraded. Re-arranging sometimes changes the symptoms, but this is usually temporary.

If you have access to an Apple-owned store, make an appointment for a free evaluation at the genius bar. Otherwise, contact an Apple-Authorized service provider (there may be an evaluation fee, but if they do work for a fee or warranty repairs, be sure to ask for a rebate of the evaluation fee).

Run Apple Hardware Test to check if it can identify any issues. You can also try resetting SMC. For further diagnosis, you need to book the appointment with Apple Genius. PS: Before handing over your device to the genius make sure to backup your internal drive.