This Bechor needs no Pidyon Haben because his father is alive.
Should his father die then the son needs to redeem himself.
Shulchan Aruch Y.D. 305:19
A כהן who had a son a בכור who was a חלל
(son the חלל loses his status as a כהן)
If the father dies within* 30 days of his son's
birth then the son needs to redeem himself.
While the father is alive, as a כהן he is זוכה for
himself the money. (No Pidyon necessary)
One reader wrote of another possibility
If the father had only 5 סלעים and both father
and son are Bechorim then the father has
to redeem himself before redeeming his son.
*If the father dies (after 30 days) then the
son puts aside 5 סלעים he doesn't hand it over
to a Kohen but gets to keep it.