When the timing of something is propitious or you've got propitious circumstances for something, it's likely to turn out well. A propitious time for taking a big test is when you've studied hard and gotten a good night's sleep.
If you believe in astrology, you might check your horoscope to settle on a propitious day for your wedding. A propitious moment to ask your parents about that spring break trip to Cancun might be when you've just unveiled your straight-A report card. If Mom's Diner down the street closed last week and the Big Bruiser Football Academy just moved in next door, the circumstances seem propitious for the grand opening of your all-you-can-eat barbecue palace and tattoo parlor.