Florida has a minimum passing distance of at least three feet. The law actually talks about how the driver has to give a cyclist a reasonable safe distance when passing. When a car comes too close and the cyclist takes evasive action to get out of the way, the cyclist has a right to seek compensation from that driver if they caused an accident.
This type of situation is a proof question because you have to prove that the car was too close to the cyclist. Sometimes there will be eyewitnesses around the accident scene and actually saw what happened. It's even possible that it could be proven because the cyclist had a GoPro or some other type of video camera.
If this has happened to you and you were injured, you should consider contacting an attorney who handles such cases because it is illegal to ride too close to a cyclist.