Learn Hardcore Croatian: Policija može uvjeriti ubojicu.

Because policija is grammatically singular in Croatian. Unlike English police, which usually takes a plural verb, Croatian policija behaves like a singular noun meaning the police force. So the verb must also be singular:

Policija može = The police can

If you meant individual police officers, you would normally use a plural noun such as policajci, and then the verb would be plural:

Policajci mogu = The police officers can

Why is uvjeriti in the infinitive?

Because after the modal verb moći = can / to be able to, Croatian normally uses the infinitive of the main verb:

može uvjeriti = can convince

This is very common in Croatian:

može doći = can come
može vidjeti = can see
može uvjeriti = can convince

Unlike English, Croatian does not use a separate word like to before the infinitive here.

What exactly does može mean here?