BE35 PLT AT 1000 FT ON STRAIGHT IN FROM THE S RPTS CRITICAL CONFLICT WITH KING AIR ON R BASE AT PAO.

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I WAS ON A 3 MI STRAIGHT-IN FINAL TO PAO RWY 31 IN LNDG CONFIGN AT APPROX 1000 FT AGL WITH CLRNC TO LAND AS #2. PAO TWR CALLED WITH A TFC ALERT OF A KING AIR AT 2 O'CLOCK POS. THE KING AIR WAS LESS THAN 1500 FT FROM US AT THE TIME. THE KING AIR PASSED SLIGHTLY BELOW (LESS THAN 200 FT) AND DIRECTLY IN FRONT OF US (LESS THAN 500 FT) FROM R TO L AS IT WAS CLBING OUT. THERE WAS NO TIME FOR EVASIVE ACTION AND NONE WAS TAKEN. THE LNDG WAS COMPLETED UNEVENTFULLY. THE KING AIR WAS APPARENTLY IN AN EXTENDED R CIRCLING 270 DEG CLBOUT AFTER TAKING OFF FROM PAO. (I DID NOT CONFIRM WITH THE TWR THAT THIS WAS THE CASE.) CONDITIONS WERE VFR; AND I WAS PERFORMING A DILIGENT SCAN OF THE AIRSPACE IN FRONT OF ME LOOKING FOR OTHER TFC BECAUSE PAO IS NORMALLY QUITE BUSY. HOWEVER; I DID NOT SEE THE KING AIR COMING IN FROM THE SIDE. EITHER THE KING AIR WAS NOT FLYING A PATH EXPECTED BY THE TWR AND/OR THE TWR WAS NOT AWARE OF THE DEVELOPING NEAR MISS AND THEREFORE DID NOT ISSUE AVOIDANCE INSTRUCTIONS. I AM NOT AWARE OF ANYTHING I COULD HAVE DONE TO AVOID THE NEAR MISS.