Oh, I always thought it was whoever arrived at the siege first. Wow, that's a pretty serious issue - unless that 1 archer who showed up must have been Samuel L. Jackson or something!
Do you have a save file of this issue? If so, please upload it. If your quota is full, use an external hosting site such as mediafire.
Are you sure it's not just a graphical bug? I had the King of England "stealing" one of my sieges, despite the fact that he was really just passing through. When the siege ended (with him as shown siege leader) I still gained the holding.
I've not been able to recreate the situation with the save file you uploaded. I always win the siege before anyone else arrives (due to them needing to fight off newly raised Shia levies). The save seems to be from several months after your screenshot too, so I'm not sure its the right one.
Also, are you using any Mods? I ask because your king has a base stewardship of 41, which is just a little more than the game normally allows. If other changes in your game alter things like levy sizes it may be hard for anyone else to recreate the situation you are reporting.
Thats why amass wealth ambition should only be able to do once with the same ruler.
I can see that he has a one man army in the siege, but he does not steal it at any point. Although the siege will end a day or two after the save since the crusade will be over.
Are you trying the second save, K-vald? With that one I was able to reproduce the issue. The first siege, where the Danes and the 1-archer army are in the same province gets won by the Danish armies. The last holding's siege gets tagged by the Slesvigian army.
OP: Did you reorganize your troops at any point during the siege? I notice you have two armies, one lead by a holy order grand master and the other lead by your king. I think I've seen weird things happen when you move troops between armies before (the sort of thing that would have lost you leadership of the siege in previous Paradox games).
Are you trying the second save, K-vald? With that one I was able to reproduce the issue. The first siege, where the Danes and the 1-archer army are in the same province gets won by the Danish armies. The last holding's siege gets tagged by the Slesvigian army.