On the board are there: 10 of clubs, 9 of diamonds, 7 of spades, 8 of diamonds, king of clubs.
tiny had a 3 of hearts and a jack of diamonds. It gives a straight starting at jack.
The loser had a jack of spades and a king of diamonds. It gives a straight starting at jack.
You win a part of the shared pot (3 200) !
The loser wins a part of the shared pot (3 200) !

Basic poker rules state that exactly 5 cards have to be taken into account; no more, no less, and it doesn't make any difference if there are cards coming from your own hand among the 5 cards retained or not.

IN this case, for both you and the bot, the 5 cards retained are the same: those making the straight: the jack of your respective hands, and then the 10, 9, 8 and 7 from the table.
So your king doesn't beat the 3; they aren't taken into account at all.

It may look counter-intuitive, but if you had the following situation, it would also have been shared pot:
Person 1: jack, jack
Person 2: 2, 4
Table: jack, 10, 9, 8, 7
Given that a straight is stronger than three of a kind.

thank you!