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(TMZ) - There may be a gigantic hole in the case against Justin Bieber ... because TMZ has learned the singer had next to NO alcohol in his system yet cops at the scene said he reeked of alcohol. 

TMZ has confirmed Justin's actual blood alcohol level ... it was .014 -- next to nothing.  Legal intoxication is .08.  Law enforcement sources told TMZ Thursday Bieber had a .04 ...  but TMZ has now confirmed that is NOT true.  He had a .014 -- an enormous difference.

Someone Justin's size would probably have higher than a .014 with a single beer.  So the question ... how could cops say they were overpowered by the smell of alcohol?

According to the police report ... the arresting officer was leaning in the car, talking to Justin just after the stop and the cop says, "I immediately smelled an odor of alcohol eminating [sic] from the driver's breath."

The police report goes on ... Justin was then arrested and taken to a holding facility, where another officer said he smelled "...the odor of an alc bev on his breath."

Justin insisted at the scene he was NOT drunk.  Cops say he failed his field sobriety test.

Sources connected to the case tell TMZ ... this could well come down to a credibility case, with Justin's people accusing cops of lying.  Fact is ... according to TMZ, the Miami Beach PD has had credibility issues in the past.  One law enforcement source confided in TMZ ... "That police force has had a zillion problems."

Photo Credit Splash News