Hypothesis: it's more likely to be cloudy given that yesterday was cloudy, than that the day before yesterday was cloudy.

cloudy.py

#!/usr/local/bin/python3

import csv

dates = []
cloudyvalues = []
pattern = []
pattern3 = []
thisdate = '11-5-2005'
thissky = []
counter = 1
with open ('data.csv', 'r') as csvfile:
  myreader = csv.reader(csvfile, delimiter=',')
  for row in myreader:
    counter = counter + 1
    if counter > 100000:
      break
    [date, time] = row[0].split(' ')
    if time not in set(['20:00:00', '21:00:00', '22:00:00']):
      continue
    if not date.startswith('9'):
      continue
    if date != thisdate:
      # Evaluate the last cloudiness and clear it
      cloudy = 0
      for value in thissky:
        if value < 5:
          cloudy = 1
      dates.append(date)
      if len(cloudyvalues) > 0:
        pattern.append(str(cloudyvalues[-1]) + str(cloudy))
      if len(cloudyvalues) > 1:
        pattern3.append(str(cloudyvalues[-2]) + str(cloudy))
      cloudyvalues.append(cloudy)
      thissky = []
    thisdate = date
    thissky.append(int(row[2]))
  
  for i in range(len(pattern3)):
    print(dates[i], pattern3[i])

  print("Total days counted: ", len(dates))
  print("Cloudy days counted: ", cloudyvalues.count(1))
  print("P(cloudy): ", cloudyvalues.count(1)/len(dates))
  print("\n")
  print("Total days after cloudy days: ", pattern.count('11') + pattern.count('10'))
  print("Cloudy days following cloudy days: ", pattern.count('11'))
  print("P(cloudy|yesterday was cloudy): ", pattern.count('11') / (pattern.count('11') + pattern.count('10')))
  print("\n")
  print("Total days, where before yesterday was cloudy: ", pattern3.count('11') + pattern3.count('10'))
  print("Cloudy days where before yesterday was cloudy: ", pattern3.count('11'))
  print("P(cloudy|before yesterday was cloudy): ", pattern3.count('11') / (pattern3.count('11') + pattern3.count('10')))