"despite the likelihood" is a correct and usable phrase in written English.
You can use it when referring to the possibility of something happening or not happening, usually when the likelihood of it happening is low. For example, "Despite the likelihood of passing the exam, she was determined to try her best."
Despite the likelihood of it having fleas, it is a winsome, beautiful horse.
Others agree to be paid to directly breastfeed the baby, despite the likelihood of bonding.
Despite the likelihood that he would be arrested on arrival, Mr. Ravalomanana was set on returning, he said on Friday.
It was another final act of desperation and this time – despite the likelihood that Garde will be remembered as the right man hired too late – it didn't work.
At that point I believed that Rodgers understood his own blueprint, and despite the likelihood of Luis Suárez's departure, I was hopeful.
These periodic crackdowns and the widespread use of execution have received broad popular support in China, despite the likelihood of wrongful convictions.
Despite the likelihood of regulatory hurdles, Germany's largest telephone company, Deutsche Telekom, is expected to announce today that it has agreed to acquire VoiceStream Wireless for $50.7 billion.
Despite the likelihood of an embarrassing rebuke for Trump, neither the House nor the Senate is expected to muster enough votes to override an expected veto.
There was no example of an open-cut mine being successfully rehabilitated, the report said, despite the likelihood of at least 45 open-cut voids across NSW.
Robert Gardner chief economist at Nationwide predicted house prices would accelerate at a modest pace, despite the likelihood of interest rate increase from the middle of next year.
Despite the likelihood that, as corporate profitability cools, the current rate of expansion in ad sales will slow, she is predicting double-digit growth in revenue for the big agencies in 2001.
