Probability would be based on average January figures for Ontario over a number of years, say, 10 years.
If over 10 years only one January was "warm", where warm was defined between 50F and 68F (10C to 20C), for example, then the experimental probability would be 0.1 or 10% (1 in 10). If the figures were over, say, 100 years, then 10% would be equivalent to 10 years in a hundred. Let's say we had the January temperatures from 1900 to 2000 and 10 of those Januarys were classed as warm, then 10/100=1/10=0.1 or 10% is the experimental probability for forecasting the temperature in January.
Other probability predictions may be based on current weather patterns and trends, like global warming, meteorological data, such as wind directions, ocean temperatures and currents, global temperatures, solar activity, volcanic activity, geothermal activity, etc., and past weather patterns. Computer models of weather patterns are often used to publish probabilities for forecasting purposes.