Problem with opacity InDesign | Illustrator

Could be related to several things.

If it's a black (K-only) screen representation issue, your "Appearance of Black" settings in Indesign can be adjusted, settings depending on your goals.

Could be your transparency blending space settings, depending of course on the placed object and how Indesign has been told to deal with whatever it is.

Could be color profile mismatch, depending again on your Indesign file's specific color profile and the color profile of the placed file and also how Indesign has been told to deal with color profile mis-matches. (Indesign might set to convert the placed file through RGB color space even if it is a native CMYK file, resulting in a "rich" CMYK build which will display differently than K-only.)

Without knowing all your color workflow and preference settings, it's hard to diagnose. But try a couple things right off: 1. Using Indesign's Separations Preview mode (Window>Output>Separations Preview, then choose "Preview" from the View pop-up menu) basically forces Indesign to render everything to CMYK visual equivalent rather than displaying various elements on the fly. It slows down screen redraw, of course, but can help you track down CMYK conversion and black rendering issues. And 2. Adding a white (paper) rectangle under your whole page renders the page to a white background rather than transparent, which can help you figure out transparency issues. Depending on your document/pref settings, this can change the screen display of transparent objects' darkness.

Sorry for the shotgun approach. There are SO MANY variables when dealing with color matching, space, profiles, and conversion.

I'm not even sure what you're asking. Can you please give us a better description?