I think the odds are smaller than that
Unless my mathematical wife can't do stats
It is actually 219/10,000 (2%) based on 43/63 each season worked our properly as the odds of not getting one ten years in a row in the FA Cup. Unless you have assumed a top two draw on Monday also?
We didn't always make it to the third round of the league cup, even when in Europe, so not straight forward to work out. Fair Play league and all that.