How to calculate probabilities when there is censoring? Suppose we have 10 patients among whom 4 readmit and 2 get censored. Then what is the probability of readmission of these patients? My intuition tells me it should be 0.5, because I couldn't observe what would happen to the censored patients if they did not get censored. So, I should exclude them from the denominator while calculating the probability with which the patients readmit? 
 A: The question of the probability of an event in a survival analysis type situation is philosophically tricky.  I believe it is generally better not to try to think in terms of probabilities here, but to try to think primarily in terms of rates.  
That said, if patients are automatically censored after a fixed period (say, one year), and all patients are observed throughout that period (no one dies of another cause, moves away, etc.), then I think it is fair to say something like, 'our estimate of the probability of readmission within one year is $40\%$'.  
On the other hand, if patients are censored at randomly varying times and for different reasons (e.g., some are lost to followup), then it is more complicated to state the probability of readmission within a given fixed period.  You could say something like, 'given that we don't have sufficient information about two patients, the point* estimate of readmission within one year can range from $40\%$ (if neither were readmitted outside of our knowledge) to $60\%$ (if both were readmitted outside our knowledge)'.  I suspect a Bayesian analysis might be useful, but the appropriate analysis for such a situation is beyond my (relatively low) level of Bayesian sophistication.  
I don't think it makes any sense to make an unqualified statement like, 'the probability of readmission is $p\%$'.  Given enough time and an infinite population, more patients would eventually readmit.  It is possible that the number would eventually asymptote to some non-0 proportion, but it also might not and, at best, we cannot say.  
* Note that I specifically state this is the point estimate, so as not to lead to confusion that these might be the limits of a confidence interval.   
