Indicates that something is very likely or probable to happen (same meaning as 可能性が高い); a common expression for making predictions.
明日は雨の可能性の高い予報が出ているから傘を持って行って。
The forecast says it's very likely to rain tomorrow, so take an umbrella.
この候補者が当選する可能性の高い理由を説明します。
I'll explain the reasons why this candidate is likely to win.
初期の検査では異常が見つかる可能性の高いケースもある。
There are cases where initial tests are likely to find abnormalities.