LESS THAN STANDARD SEPARATION BETWEEN 2 ACR ACFT. OPERATIONAL ERROR DUE TO ARTCC CTLR DISTR TASK.

Narrative

I WAS WORKING 4 ACFT IN MY AIRSPACE AS A CTLR AT ZMA. I RECEIVED A HDOF ON ACR Y FROM EWR TO MKJP AT FL350. AT THE SAME TIME AS THE HDOF; THE PREVIOUS SECTOR AT ZJX COORDINATED THE FACT THAT ACR Y WAS OVERTAKING AN ACFT I HAD PREVIOUSLY RECEIVED A HDOF ON (ACR X). THE CTLR AT ZJX ASKED IF ACTION WAS REQUIRED TO MOVE ACR Y TO MAINTAIN SEP. I EXPLAINED THAT THEY PRESENTLY HAD 65 MI LAT SEP AND THAT IF SOMEONE NEEDED TO BE MOVED THAT I WOULD DSND ACR X (WHO WAS LNDG AT MIA). I WENT ON TO OTHER BUSINESS OF THE SECTOR; NAMELY MONITORING AN APCH TO THE BACKCOURSE 27 AT MLB AND WAS INADVERTENTLY DELAYED IN TAKING ACTION TO CORRECT THE OVERTAKE SITUATION. IN REFERRING BACK TO THE SITUATION; OUR AIR TFC C/A SYS HAD BEEN ACTIVATED. I QUICKLY ISSUED AN IMMEDIATE DSCNT CLRNC TO FL330 TO ACR X AND THE PLT ACKNOWLEDGED ALSO STATING HE HAD ACR Y IN SIGHT. I ALSO TURNED ACR Y TO HDG 240 DEGS; UPON ACKNOWLEDGEMENT ALSO STATED HAVING ACR X IN SIGHT RELIEVING THE CHANCE FOR A NEAR MIDAIR. THE PLTS WERE VERY PROFESSIONAL AND COOPERATIVE; BUT MINIMUM SEP STANDARDS WERE LOST. CLOSEST PROX WAS 3 MI LAT AND 500' VERT.