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Business Segment Information - Reconciliation of Segment Adjusted EBITDA to Net (Loss) Income (Detail) - USD ($)
$ in Millions
 3 Months Ended 6 Months Ended
Apr. 30, 2020
Jan. 31, 2020
Apr. 30, 2019
Jan. 31, 2019
Apr. 30, 2020
Apr. 30, 2019
Segment Reporting Information [Line Items]            
Interest expense, net $ (7.3)   $ (8.0)   $ (14.6) $ (15.8)
Benefit (provision) for income taxes 10.1   (2.5)   12.7 1.9
Restructuring costs (6.1)   (1.8)   (6.7) (2.9)
Stock-based compensation expense         (5.5) (4.8)
Loss on sale of business (8.8)       (8.8)  
Gain on acquisition of business 11.9       11.9  
Impairment charges     (0.1)     (2.8)
Net (loss) income (7.6) $ (9.4) 5.6 $ (14.6) (16.7) (9.0)
Corporate and Other [Member]            
Segment Reporting Information [Line Items]            
Adjusted EBITDA (9.5)   (11.0)   (17.5) (21.2)
Operating Segment [Member] | Fire & Emergency [Member]            
Segment Reporting Information [Line Items]            
Adjusted EBITDA 10.2   15.1   12.1 23.4
Operating Segment [Member] | Commercial [Member]            
Segment Reporting Information [Line Items]            
Adjusted EBITDA 8.0   14.7   17.9 19.7
Operating Segment [Member] | Recreation [Member]            
Segment Reporting Information [Line Items]            
Adjusted EBITDA (1.1)   17.3   5.9 26.5
Reconciling Items [Member]            
Segment Reporting Information [Line Items]            
Depreciation and amortization (10.9)   (11.6)   (21.7) (23.8)
Interest expense, net (7.3)   (8.0)   (14.6) (15.8)
Benefit (provision) for income taxes 10.1   (2.5)   12.7 1.9
Transaction expenses (0.9)       (2.0) (0.2)
Sponsor expense reimbursement     (0.1)   (0.1) (0.6)
Restructuring costs (6.1)   (1.8)   (6.7) (2.9)
Stock-based compensation expense (2.9)   (3.4)   (5.5) (4.8)
Legal matters (1.4)   (2.4)   (1.5) (4.5)
Loss on sale of business (8.8)       (8.8)  
Gain on acquisition of business 11.9       11.9  
Impairment charges     (0.1)     (2.8)
Earnings (losses) attributable to assets held for sale $ 1.1       1.3 (1.7)
Deferred purchase price payment     $ (0.6)   $ (0.1) $ (2.2)