I have a set of 50,000 time series lasting 31 years (each time series for each of 50,000 cells). I would like to find the probability that the next year will go to 0 given the values in previous years.
If you assume that you actually can use previous data to infer future data, then: learn the statistical distribution and use it to predict the probability of a future value. A simple recipe would be to take all data and sort it into bins, with each bin index representing one of the possible values in that series, normalize the counted values (i.e. divide the count you got by the total amount of samples) and you get the probability for each of the values.
P.S. don't use this for the stock market :)