Why didn't the convict believe that there was any good in the world?

I imagine you are referring to the character of Valjean. Valjean goes into prison an innocent man. Sure he stole food but it was for his impoverished family. For this act of desperation, he is sent to prison for 5 years. The other fourteen years he got was because of his repeated attempts to escape prison to see and help his family. Valjean comes out of prison a much harder man. Life has been unfair to him and he must face more injustice for much of the rest of the play. The poor guy cannot get a break!