An "ominous voice" refers to a deep or eerie tone that creates a feeling of danger or foreboding. It suggests that something bad or threatening is likely to happen. Full definition
Lots of ominous voices and sound effects I hope. (lawyerist.com)
Meanwhile the announcer / ominous voice says «We can't say for sure that this man's lung cancer was from smoking, but who would doubt it,» or something similar (such as «We can't say for sure that this man's lung cancer was from smoking, but the more he smoked, the more likely it is.») (dotearth.blogs.nytimes.com)