A320 FLT CREW DURING VISUAL APCH TO RWY 25L LAS FOLLOWED WRONG ACFT TO RWY.

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I WAS THE PNF IN TRAIL BEHIND 2 OTHER ACFT ON THE DOWNWIND FOR RWY 25L; LAS. AS WE LEVELED OFF AT 6000 FT; VEGAS APCH ASKED US IF WE HAD THE 'FALCON JET' IN SIGHT. I SAW AN ACFT AT OUR 11 O'CLOCK POS AT ABOUT 5 MI. I ASKED THE FO (PF) IF HE HAD THE TFC. I TOLD HIM I SAW IT THERE AT 11 O'CLOCK POS LOW. HE THEN SPOTTED THE SAME ACFT AND TOLD ME. I TOLD ATC THAT WE HAD THE 'FALCON JET AT 11 O'CLOCK POS AND THE RWY IN SIGHT....' ATC THEN SAID; 'CLRED THE VISUAL APCH TO RWY 25L BEHIND THE FALCON JET....' BOTH THE FO AND I SAW NO OTHER ACFT IN FRONT OF US; NOR WERE WE INFORMED THAT WE WERE 1 OF 3 ACFT IN TRAIL. AS THE ACFT THAT WE SAW STARTED ITS DOGLEG TURN; WE BEGAN OUR BASE TURN; AND I THEN SET 3800 FT FOR THE RELIN OM; AS PER SOP. SHORTLY THEREAFTER; WE BEGAN OUR DSCNT WHILE WATCHING THE ACFT IN FRONT OF US. JUST AS WE DSNDED THROUGH 5300 FT; ATC TOLD US THAT WE WERE FOLLOWING 'THE WRONG ACFT.' THEY TOLD US TO MAINTAIN 6000 FT; AND TURN L TO A HDG OF 350 DEGS; WHICH WE IMMEDIATELY COMPLIED. WE BOTH (FO AND I) THEN SAW THE REAL 'FALCON JET' AT OUR 2 O'CLOCK POS AND ABOUT 2 MI; ALSO IN A L TURN TO BASE. THE OUTCOME WAS THAT WE BOTH MISTOOK THE ACFT IN FRONT OF THE FALCON JET AS OUR TFC TO FOLLOW. ATC ASSUMED WE HAD THE ACFT BTWN US IN SIGHT. APPARENTLY WE WERE #3; THE FALCON JET WAS #2; AND THE RJ WAS #1. WE DID NOT SEE #2; AND THOUGHT #1 WAS OUR TFC TO FOLLOW. WHEN WE TOLD ATC WE HAD THE FALCON JET IN SIGHT; WE BOTH THOUGHT WE DID; AS NONE OF US SAW ANY OTHER ACFT. I SPOKE TO ATC UPON LNDG AND THEY TOLD ME THAT THEY DO NOT LIKE ISSUING VISUAL APCH CLRNC ON DOWNWIND FOR THE VERY REASON THAT WE EXPERIENCED -- ESPECIALLY IF THERE ARE A SERIES OF ACFT IN TRAIL. FROM A HUMAN FACTORS STANDPOINT; CLRLY THERE WAS A MISIDENT OF THE ACFT WE WERE TO FOLLOW ON THE VISUAL. ATC DID NOT CATCH IT UNTIL WE BEGAN OUR TURN AND THEY SAW THAT WE WERE TURNING INSIDE OUR TFC. ATC COULD HAVE TOLD US THAT WE WERE #3 IN TRAIL BEHIND AN RJ AND A FALCON JET; FOLLOW THE FALCON JET; CLRED THE VISUAL RWY 25L. HAD THEY SAID THAT; WE WOULD HAVE THEN KNOWN THAT SOMETHING WAS WRONG; BECAUSE WE ONLY SAW 1 AIRPLANE IN FRONT OF US.