The doctor's patients

When the doctor's surgery opens, on Monday morning, there are three people
queueing outside. Each person is waiting to see a doctor. They each speak
to the receptionist and then take a seat in the waiting area.

The waiting area has five seats arranged in a single row, with seats side-
by-side. Initially all seats are unoccupied. Each patients selects a seat
at random, with the proviso that they prefer not to sit next to a seat
that is already occupied by another patient.

What is the probability that all three patients get a seating position
they are happy with i.e. not seated next to another person?

--
David Entwistle