You will only rarely have complete solitiude if you choose to use the shelter system or camp at established campsites. You're going to pass people throughout the day and people are going to pass you. But if you don't stay at shelters you'll probably see 1/2 dozen people a day. Reason being is you can be an hour ahead of someone or an hour behind them and if you are hiking at about the same pace you'll never meet. So there can be 30 people on the trail within a day's walk of where you're at and you'll only ever encounter a few of them. Beyond that you'll encounter people as you choose to.