* "If the king and prince own different carriages..." This uses the definite article "the" to refer to specific, already known individuals. This implies that the reader is aware of who the king and prince are.
* "If a king and a prince own different carriages..." This uses the indefinite article "a" to refer to any king and any prince. This suggests a general statement about kings and princes, not specific individuals.
* "If a king and prince own different carriages..." This is similar to the previous option but uses "a" for the king and the definite article "the" for the prince. This could be used if the reader is aware of a specific prince but not a specific king.
It's important to understand the context and intended meaning to choose the correct pronoun.