Australia doesn’t have a huge mountain range like the Andes that collects all the rain from clouds blowing across the continent. The driest desert in the world, the Atacama, is on the western side of the Andes between the same latitudes as Australia.
If you look at which latitudes where Australia lies in relationship to South America. It lies between 9° and 44°S. That is the region where most winds bearing rain clouds come from the south East or north East similar to South America.
Australia's latitude in Perspective
The Andes range is almost 7000m tall and still growing. Rain clouds don’t travel high enough to cross it. Thus almost all of the rain in those latitudes falls on the eastern slopes and becomes the rivers of the Amazon basin while the Atacama desert on the western side gets none.
Sadly, Australia is the most ancient continent and all our high mountains have long since worn away. So our rainfall pattern is reversed. A narrow strip of green along the East coast gradually fading to desert the further west you travel. It’s a similar pattern if you compare Australia with southern Africa at the same latitudes, the Kalahari desert and Namibia on the west and a strip of green along the east coast. Climate and Vegetation of Africa
Atacama desert in Chile - below Simpson Desert Australia
Kalahari
“A rain shadow is a dry area on the leeward side of a mountainous area (away from the wind). The mountains block the passage of rain-producing weather systems and cast a "shadow" of dryness behind them.”