jmc

Simplifying each term in $P,$ $$P=\left(\frac{1}{2}\right)\left(\frac{2}{3}\right)\left(\frac{3}{4}\right)\cdots \left(\frac{n-1}{n}\right).$$The denominator of each fraction cancels with the numerator of the next fraction, so $P=\frac{1}{n}.$ When $n=2007,$ $P=\boxed{\frac{1}{2007}}.$