Final answer:
The family in John 4:53 believed in response to the news they received, which typically would involve witnessing Jesus's miraculous works. However, without the specific scripture from John, a detailed answer can't be provided.
Step-by-step explanation:
According to John 4:53, the family's response to the news was that they believed.
In the context of the scripture, this belief likely resulted from witnessing or hearing about a profound event that would affirm their faith, such as a healing or miracle attributed to Jesus.
Although you have provided various scripture and literature references, none of them directly quote John 4:53 or detail the reaction of a family to news in that context, therefore, a specific passage is needed from the Book of John to give a precise answer.
The provided texts mention interactions and reactions in different scenarios that do not directly correlate with John 4:53.