I was a nail biter.. Terrible habit, I also was under a lot of stress at home.. My father was always angry and I was always worried he would blow up. .. Not saying your child is, but it gave me something to sooth myself..
I was finally able to break the habit, when a beloved aunt asked me about my nails. She said "your mother has such beautiful nails.. I bet you do too.. If you will grow them out I will polish them for you.."
This intrigued me.. so I really had to concentrate to quit biting them.. Thank goodness my nails grow pretty fast, so I saw results fairly quickly..
3 is young so he will need your help. Take his fingers out of his mouth without a word each time you see hm doing this.
Do find the cremes or polish that you can place on his fingers.. this will be his own reminder..
Most of all it will take total commitment from you and those around him, to give him the signal or remove his fingers each time you witness it.
If you think he needs a replacement to sooth him or comfort him.. find something you can live with.. Maybe teething beads he can wear..