Analysis of user login activity to the DBX digibank app showed that the times elapsed between two logons are independent and exponentially distributed with mean

\(1 / \lambda\). Find the CDF of the time \(T-T_{N_{T}}\) elapsed since the last logon before time \(T\), given that the user has logged on at least once.
The number of logins until time \(t>0\) can be modeled by a standard Poisson process \(\left(N_{t}\right)_{t \in[0, T]}\) with intensity \(\lambda\).