I have a simple problem driving me crazy

the topic is stochastic process and markov process, this is the problem:

i've tried few approaches but nothing comes out, i know its simple, will be happy for assistance. thanksassuming every day's weather has only two options: rainy or sunny.

the probability that in certain day the weather is the same as the day before is \(\displaystyle p\). the probability of change in weather is \(\displaystyle q=1-p\).

now i will define \(\displaystyle (x_{[n]})_{n>=0}\) as a discrete time stochastic process as: \(\displaystyle x_{[n]}=1\) if the n'th day was rainy and \(\displaystyle x_{[n]}=0\) if the n'th day was sunny.

the question is: given that today, n=0, is a rainy day, find the probability to rain in the n'th day. clue: you can organize the data in a matrix.