How to generate random dates based on the probability of the days in Python?

I would like to generate a random list of length n based on the dates of, say, September. So, you have your list like this:

september = ["01/09/2019","02/09/2019",...,"30/09/2019"]

And I would like to generate a list that contains, say, 1000 elements taken randomly from september like this:

dates = ["02/09/2019","02/09/2019","07/09/2019",...,"23/09/2019"]

I could use something like:

dates = np.random.choice(september,1000)

But the catch is that I want dates to be selected based on the probabilities of the days of the week. So for example, I have a dictionary like this:

days = {"Monday":0.1,"Tuesday":0.4,"Wednesday":0.1,"Thursday":0.05,"Friday":0.05,"Saturday":0.2,"Sunday":0.1}

So as "01/01/2019" was Sunday, I would like to choose this date from september with probability 0.1.

My attempt was to create a list whose first element is the probability of the first date in september and after 7 days this probability repeats and so on, like this:

p1 = [0.1,0.1,0.4,0.1,0.05,0.05,0.2,0.1,0.1,0.4,0.1,0.05,0.05,...]

Obviously this doesn't add to 1, so I would do the following:

p2 = [x/sum(p1) for x in p1]

And then:

dates = np.random.choice(september,1000,p=p2)

However, I am not sure this really works... Can you help me?