Considering what Harry comes from, his experiences with his family and his Aunt Marge, it should be hard for him to trust people. You would expect someone from that background to be stunted in many ways.
We already know he has found close friends at Hogwarts in Ron and Hermione, and he trusts Dumbledore. The three of them are all dependable, and there is no known reason to not trust them.
Harry finishes the summer living in The Leaky Cauldron, doing his homework with the help of Florean Fortesque, a local ice-cream shop owner, and becoming well acquainted with all of the shops and store owners. On the last day, Hermione and the Weasleys show up to buy their school supplies and stay in the same inn as Harry.
Late that night, while everyone is packing, Harry runs down to the dining room to grab something of Ron's for him and overhears Mr and Mrs Weasley arguing. He goes to pass them by when he hears his own name and stops.
Molly and Arthur Weasley are discussing the recent jailbreak from the wizarding prison, Azkaban. Sirius Black, an insane former Death Eater, is pursuing Harry. Blamed for Voldemort's fall, he thinks killing Harry will bring him back...
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Harry Potter and the Prisoner of Azkaban