Let's start with the 24-h precipitation totals ending 9 PM on Friday (see below). A few hundredths of an inch over central Puget Sound, while a few dozen miles to the east along the western Cascade slopes some locations got more than 3 inches. The origin? A rain shadow in the lee of the Olympic Mountains. If you look carefully you will see very light precipitation to the east of the mountains of Vancouver Island, which has its own rain shadow.
The reason for this profound rain shadow to the east of the Olympics? We have quite strong westerly flow over us, flow that was associated with a disturbance originating in the Gulf of Alaska. To illustrate, here are the winds, temperatures, and heights of the 850 hPa pressure surface (about 5000 ft above the surface). 30-40 knot westerly to west-northwesterly flow hitting the Olympics. Where the winds take air upwards, you get enhanced precipitation. Where the air is rapidly descending (east of the Olympics), precipitation is attenuated.
The air still has water vapor in it even when precipitation is not falling; as the air is forced again to rise (this time by the Cascade), torrential rain and snow results.