Learn Finnish: Etsivä ei liene uskonut alibia. - The detective probably hasn't believed the alibi.

It is built with three parts: the negative verb ei, the special potential auxiliary word liene (which is the potential connegative form of olla), and the active past participle of the main verb, uskonut. Together, they express that something probably hasn't or probably didn't happen.

What is the difference in meaning between ei liene uskonut and the present potential ei uskone?

Ei uskone is the present potential negative, meaning "probably doesn't believe" right now. Ei liene uskonut uses the perfect tense to shift the doubt into the past, meaning "probably didn't believe" or "probably hasn't believed" at the time of the investigation.

Is alibia in the partitive case because the sentence is negative?

While negative sentences do generally force the object into the partitive, you would use the partitive here anyway because of the verb. The verb uskoa (to believe) always requires its object to be in the partitive case, even in a positive sentence like Etsivä uskoi alibia.

The word etsivä looks like a verb form. Is it?

Yes, etsivä is the active present participle of the verb etsiä (to search or look for). Literally meaning "the searching one" or "the one who searches", it has become an established noun meaning "detective".