how to work out probabilities ?

It depends on whether each event is independent. An example of an independent event is like a coin flip; it's always 50/50 heads/tails regardless of the previous flip. Is there a theoretical probability of event 1 vs. event -1?

If we assume that the theoretical probabilities are 50%/50% then the chances of two 1 events in a row are 25%. The probability of two -1 events in a row is also 25%. (1 then -1 is 25%; -1 then 1 is 25%.)

In your data the empirical chances of a 1 is 53.4% and -1 is 46.6%. If we use these probabilities then the chances of two 1 events in a row is 53.4% x 53.4% = 28.5%. The chances of two -1 events in a row is 46.6% x 46.6% = 21.7%.

If the events are not independent then there is not enough information to answer your question theoretically, although we can make an educated guess from your data. The number of times that 1 occurs twice in a row is 440. 440/1571 = 28.0%. The number of times that -1 occurs twice in a row is 333/1571 = 21.2%.