Where do I even begin.

I second everything lasersniper says apart from they should be naked in all of them, can't just be strangers anymore after you've seen each other's goolies

Haha but on a more serious note did the others travel there specifically for an event or the festival or did they just happen to be visiting at the time?

If there is a specific activity they are there for it could have a prize or pot, it could be the main activity from which the festival gets its reputation or name. One character sees someone acting shady and cheating and as they are all invested in it they all will choose to do something about it. Or the prize/pot could be stolen and so they need to retrieve it so the festival isn't ruined. Maybe even the native characters family or friend owns the stand or activity which stuff is taken from so he's doubley invested and is therefore grateful of the help of the other two.

Another idea is that one of the activities requires a team and if they wish to participate in it they need to join together to make up their numbers.

Festival's being busy places someone could have a child go missing and so they could band together to find them, it could even end up being a ruse to have the players wander down shady alleyways and get robbed or captured so they have to work together to get their stuff back or escape. They could even get away themselves but realise other people probably got caught and have to track down the kidnappers anyway or they could all fall for the same missing child trick seperately and end up bumping into each other whilst trying to track down the criminals.

No problem. That is why we gather here, to help one another. Let us know how it turns out.

Update!
They actually just fell for my bait, right off the bat. There is a sickness in the town that was "caused by" a witch, and when the Lord of the town summoned brave adventurers to the call, they were already invested enough as characters to meet and sign up to go hunt this "evil" witch down. They did have a comical exchange at the Goblin dunk tanks, so they were fairly familiar with each other. Sometimes players make your job easy. Thanks, players! And thank you Sidera and Lasersniper for the help!

This. Last session I prepped a low-tier villain that tied into one of my PC's backstory(rouge). Player got so pumped she poured everything into one punch and killed him straight off. One hour of prep gone in 30 seconds. Felt glorious though