Need help coming up with conflict.

So, I have a really kinda weird idea. basically my story takes place in a world that's inhabitants call Point of Origin, or Origin for short, and its basically the centre of every universe, connected to all of them. And its inhabitants are… well spirits of a sort. They're the embodiment of certain things. 'Clear Nights Sky', 'Contented Silence of Lovers', 'Death of a Star', 'Small Magical Fire, and so on and so forth. the world itself is a series of islands in a sort of spiral pattern, each having a certain theme. e.g. Clear Night Sky lives on the isle of Night, Contented Silence of lovers lives on the isle of Void, Death of a Star lives on the isle of Death and Small magical fire lives on the isle of magic. the story has three protagonists: Evelyn, a girl from modern day earth, Eris, a prince from a high fantasy world, and Alaesya, a Space Mercenary from a sci-fi world. Each of them end up in Origin in separate locations, on different isles. No one has ever entered Origin before and they discover that they can travel between Origin and the rest of the universes by using doors, which only appear for significant events, like the death of a beloved monarch, or the birth of a star, or a storm of catasrophic power and destruction.

The problem I now face is that I have no source of conflict for these three. I know I want them to make their own friends and allies in Origin, and that they're not necessarily even on the same side, but beyond that I have no idea. So any ideas are welcome, just make them… grand.

Maybe the mercenary was hired to kill the prince?

I think that all conflict is generated by character goals. Give each character something they would kill for/die for. Then take that thing away and let the conflict begin. Give them clashing goals. If the prince is an idealist who wants to rid the world of all evil then he will immeditatly have conflict with the mercenary who kills for a living. maybe evelyn wants nothing more than to go to the sci-fi world and become a space pirate, so she and the mercenary becomes rivals. IDK! There is so much to build off of!

I recognize the sort of plot structure you're attempting to build; it reminds me of how Leigh Bargudo and George R R Martin write, where they introduce totally different characters in totally different situations and the story is about how their individual plotlines intertwine. First, ask yourself some questions:

1. Are these people friends? Enemies? Lovers? What is their relationship? How do you plan to bring them together and build on their relationships?
   Note: The characters backgrounds are incredibly different, so I would be careful about letting them get along too smoothly. They are allowed to have flaws, and I bet that differing mindsets would be one of them. If the prince comes from a realm at all resembling Earth (and most fantasy realms do,) chances are he's a little it of a sexist, which would clash with both female's strong sense of independence. Think about that.
2. What are their individual goals? They need to have something they want like @TryToDoItWrite mentioned. The Mercenary might be out to make money trying to protect her little sister, while the price might be attempting to escape an arranged marriage.
3. How do their goals lead them to Origin? What happened that allowed them to travel there? You mentioned the death of a king… Maybe the prince was sucked into Origin against his will after the death of his father.

Now, here's a few tips and comments I have:

1. I find it hard to believe that these three are the first to enter Origin. Try possibly incorporating myths about disappearances and other realms into your character's cultures. For example, we earthlings have myths about women being taken to fairy courts, the Bermuda Triangle, etc…
2. You asked for ideas about conflict. I have an idea: the reason that Evelyn is in the Origin is because she's noticed things: stuff is disappearing. The stars have stopped twinkling, the wind has stopped howling, people have stopped being contented in their silences. I think that either 1) Some sort of disease is spreading through the Origin, killing spirits that can't defend themselves, that don't really have any concrete presence or 2) the spirits are killing each other.