This is one of the harder conversations a parent has to navigate, and how you handle it matters for your children's relationship with their father long after this period is over.
The most important rule is to keep your own hurt and anger out of the explanation you give the children. Whatever happened between you and their father is separate from who he is to them, and children who hear negative things about a parent from the other parent carry that damage in ways that surface years later. Your feelings are valid and real, but this conversation is about them, not about what he did to you.
Keep the explanation simple and age appropriate. The cost and the distance are honest reasons that children can understand without being burdened with adult conflict. Something as straightforward as explaining that the trip is too far and too expensive right now, and that you want to find other ways for them to stay connected, gives them a truthful answer that does not require them to take sides or process information they are not ready for.
Encouraging them to write letters is one of the most constructive things you can offer as an alternative. InmateAid makes it easy for children to send letters and drawings without your home address appearing on the envelope, which matters given the no contact situation on your end. Their relationship with their father can continue through mail even if visits are not possible, and that connection is worth preserving for their sake regardless of what is happening between the two of you.
When he is released, the relationship they have with him will be shaped in part by what you allowed during this period. Protecting that possibility, even when you are hurt, is one of the most meaningful things you can do for your children.