You can say this without actually harboring a bias against police officers: the courts do give the police the benefit of the doubt in civil rights cases. We call it qualified immunity and arguable probable case.
The case is Arrington v. City of New York, a summary order decided on October 15. Qualified immunity means the police cannot be sued for damages if the case law was not clearly established at the time of the incident, or if the police actions were objectively reasonable under the circumstances. Bearing in mind that probable cause is a defense to any false arrest case, this means the police can avoid the lawsuit if they had arguable probable cause, which exists when "either (a) it was objectively reasonable for the officer to believe that probable cause existed, or (b) officers of reasonable competence could disagree on whether the probable cause test was met."
Plaintiff sues for false arrest after he was arrested for shooting someone. He says it was in self-defense, just like the Bob Marley song. Since he admitted to the shooting, that admission would normally constitute probable cause in the absence of his self-defense claim. But "the extent to which a police officer must credit a self-defense claim is not clearly established, and depends on the facts and circumstances of each arrest. While the police cannot disregard plainly exculpatory evidence when establishing probable cause, if he as a reasonable basis for believing there is probable cause, he is not required to consider plausible defenses offered by a suspect prior to making an arrest."
So, while plaintiff's self-defense claim was plausible, "on the facts alleged in the complaint, including the absence of witnesses to corroborate the self-defense claim," the Court of Appeals (Sack, Chin and Droney) says "officers of reasonable competence could disagree on whether the probable cause test was met." In other words, plaintiff may be right that he had a self-defense claim to the shooting. But since a reasonable officer could disagree on this, plaintiff has no case.