Short of rephrasing the sentence (which is possible), most style guides address this by suggesting putting a space between the apostrophe and quotation mark in order to make the presentation clearer to readers.
The "professionals'" confidence was badly shaken by the market crash.
The "professionals' " confidence was badly shaken by the market crash.
With access to typesetting tools, you can also use what's called a thin space, which is not as wide as a regular full-sized space. This retains the separation between the apostrophe and quotation mark without it looking like there's to much of a gap. But I can't demonstrate that, because this site seems to treat the thin space character as just a regular space.
From The Chicago Manual of Style, 6.11 [paywall]:
When single quotation marks are nested within double quotation marks, and two of the marks appear next to each other, a space between the two marks, though not strictly required, aids legibility. For print publications, typesetters may place a thin space or a hair space between the two marks (as in the print edition of this manual). In electronic environments (including manuscripts submitted for publication), a nonbreaking space can be used (as in the online edition of this manual); such a space will prevent the second mark from becoming stranded at the beginning of a new line.