For avid birdwatchers, the elusive yellow bellied sapsucker is often hard to spot. Scientists at the American Birding Association have determined that there is a higher likelihood of spotting a particular bird if it has been spotted in an area the day before. For the yellow bellied sapsucker, if it is spotted on a particular day, then there is a 60% chance that it will be spotted the next day and if it is not spotted on a particular day, then there is only a 30% chance that it will be spotted on the next day. Determine the associated transition probabilities matrix and the equilibrium probability of spotting a yellow bellied sapsucker on any particular day.