An amusing string of hands

[SpaceAce]

I know the answer to this question is simple math but I am hoping someone will work it out here in this thread because I think the mechanics of the problem are interesting, especially when you factor in some of the finer details such as additional draws I flopped and what my opponents were holding. This is an actual series of four hands I played a couple of weeks ago.

The summary: In four hands, I was dealt Ah Kh three times. Every single time, I flopped a flush draw (sometimes with a little something extra) and two overcards and every single hand ended with me having no pair and no flush.

The specifics:
Hand #1: The flop was Th Jh X? giving me a gutshot Royal draw to go with everything else.
Hand #2: The flop was 3h 5h X? giving me vague wheel and steel wheel draws in addition to the flush draw and overcards.
Hand #3: This is the hand I did not get Ah Kh.
Hand #4: The flop was Xh Yh Zs. This hand was won by another player with As Ks who made his backdoor flush.

So, what are the chances of getting that specific hand three out of four times, flopping a flush draw each time and never so much as pairing up by the river? What if you add in the other draws? This problem might be too straightforward to actually interest anyone but I think it's pretty cool, especially when you factor in the big draws I flopped every time and the weird outcome of the last hand.

SpaceAce