  Here, I discuss the cosmological constant (CC) problems, in particular paying
attention to the vanishing cosmological constant. There are three cosmological
constant problems in particle physics. Hawking's idea of calculating the
probability amplitude for our Universe is peaked at CC = 0 which I try to
obtain after the initial inflationary period using a self-tuning model. I
review what has been discussed on the Hawking type calculation, and present a
(probably) correct way to calculate the amplitude, and show that the
Kim-Kyae-Lee self-tuning model allows a finite range of parameters for the CC =
0 to have a singularly large probability, approached from the AdS side.
