It's not just on the word of Jill. Yes, at first it's just her story but the cops would certainly be interested (especially since Abe had tried to murder her, obviously for a reason) and an investigation would confirm most of her story. Another student witnessed Abe in the science lab, which he did not have access to, after hours. He told her he was researching poisons and the lab contains cyanide (perhaps the lab even kept inventory in which case it might be discovered some was missing and unaccounted for). An investigation would also lead the police to learn Abe was having an affair with an instructor in the science department and under interrogation, Rita would probably admit she had "lost" her key to the lab around that time and had certain suspicions (she also has no motive to cover for Abe because he is dead). Abe was seen by Paul awake at an unusually early hour, leaving campus the morning of the murder.
Now Abe's motive would seem pretty bizarre but there is also evidence of his obsession with the judge in his copy of "Crime and Punishment." Other professors in the department and folks on campus as well as Abe's writings would give psychologists an insight into his character and paint a picture of someone who was mentally deteriorating. And again, he tried to kill his ex-girlfriend...
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