How to model a binary classification problem in a evolving environment
If you are trying to predict something that looks like probabilities, but don't actually need a "real" probability (for instance, if you aim at ranking observations to find those who are the most likely to switch to no), you could probably use logistic regression over the dataset. This would require the model to be refitted every once in a while.

If you are looking for actual probability, it has to be a probability to switch from NO to YES over a period of time. In that case, you are falling into time series analysis. This is a more complicated problem.

My intuition would be to consider the state change as a physical random phenomenon, such as a radioactive decay, where the probability of having decayed over a $\Delta t$ time period is $e^{-\lambda \Delta t}$. Based on cases who have switched in the past, you could build a rgression model to predict a $\lambda$ value for each observation. Of course you can use other decay functions than the exponential (find the best one through the validation step). This will eventually allow predicting a switch probability over any given time period.