I was just wondering. Exactly how will Gravity Probe B know the Earth bends space-time?

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This site sort of describes how it works.

NASA

As the GPB orbits the Earth it will keep itself pointed at a single bright guide star (bright in microwave energy, not visible light). At the beginning all four of its extremely sensitive gyroscopes will be aligned with this orientation. As it orbits the Earth, the reletavistic effects of Earth's gravitation field should become apparent in the drift from the initial alignment that the gyroscopes experience. The most important they are measuring is the frame dragging effect where the gravity field of the Earth will drag space-time along as the Earth rotates on its axis - losing a little time and space over the peroid the GPB will be working. The scientists will then compare the amount of drift in the gyroscopes predicted by Einstein's equations to the actual drift measured by the GPB to determine if Einstein was right. So far, he's passed every other test with flying colors.