Final answer:
The correct pronoun is "they" in the objective case.
Step-by-step explanation:
The correct pronoun for the sentence "Alex finds it is difficult to believe that (they, them) were not involved" is they, and it is in the objective case. Objective case pronouns function as objects in a sentence. In this case, "they" is the object of the verb "believe", so it is in the objective case.
Pronoun case refers to the form a pronoun takes based on its grammatical role in a sentence. In English, pronouns change their form depending on whether they function as subjects, objects, or possessive determiners.