Ask Questions ...
Take the three conflicts presented to you and ask the standard who, what, why, when, where, and how questions. Answering these questions will lead to new questions.
Focus on the relationship between the conflicts—how they tie together.
An Example ...
In about five minutes (and 15 to flesh it out) I came up with the following story idea:
A college professor is forced to receive a personal RFID implant in order to keep her job. No student, faculty, or visitors of any kind can go on campus without one. It's part of Homeland Security's new policies to alleviate crimes on college campuses. The professor's husband also receives one.
One night she works late at her office, grading term papers. When she finishes for the evening and leaves, she is surrounded by the police. They charge her with the murder of one of her students. Their evidence is based on tracking her whereabouts with the RFID.
Her husband admits to having an affair with the student (she cannot even process this, to her it's unbelievable). He, too, was at the building the evening of the murder, but tracking shows him leaving before the murder takes place.
Through the course of the story we discover that a car left the scene of the crime at the same time of the murder. Its GPS shows this. The anomaly is that nobody seems to be driving the car ... in other words the person driving it doesn't have an implant.
So, the same technology that erroneously makes her the prime suspect must be used to to rescue her.
This could use a lot of cleanup and tightening of the story telling, but that's not the point of this exercise. The point is, all of this came from the three conflicts: