In theory, and fortunately in practice, when the DNA is allowed to re-anneal, the probe competes for the binding, but only where it mirrors a complimentary sequence. Thus, RNA will attach to the location on the chromosome where the code for its production is to be found. DNA will anneal to either RNA which is still attached to a chromosome, or to the complimentary sequence DNA strand within the chromosome. Since the probe is radioactive, it can be localized via autoradiographic techniques.
The whole protocol for Chromosome in situ hybridization is available at: